The plate is made of steel having a density of 7910 kg/m3 .If the thickness of the plate is 9 mm , determine the horizontal and vertical components of reaction at the pin A and the tension in cable BC.

Answer:

a.  the temperature (K) at state 2 is  [tex]\mathbf{T_2 =270.76 \ K}}[/tex]

b.  the pressure (kPa) at state 2 is   [tex]\mathtt{ \mathbf{ p_2 = 81.79 \ kPa }}[/tex]

c.  the specific enthalpy (kJ/kg) at state 2 is [tex]\mathbf{h_2 = 271.84 \ kJ/kg}}[/tex]

d.  the temperature (K) at state 3 is   [tex]\mathbf{ T_3 = 532.959 \ K}[/tex]

Explanation:

From the given information:

T1 (K) = 249

P1 (kPa) = 61

V1 (m/s) = 209

rp = 10.7

rc = 1.8

The objective is  to determine the following:

a. Determine the temperature (K) at state 2.

b. Determine the pressure (kPa) at state 2.

c. Determine the specific enthalpy (kJ/kg) at state 2.

d. Determine the temperature (K) at state 3.

To start with the specific enthalpy (kJ/kg) at state 2.

By the relation of steady -flow energy balance equation for diffuser (isentropic)

[tex]h_1 + \dfrac{V_1^2}{2}=h_2+\dfrac{V^2_2}{2}[/tex]

[tex]h_1 + \dfrac{V_1^2}{2}=h_2+0[/tex]

[tex]h_2=h_1 + \dfrac{V_1^2}{2}[/tex]

For ideal gas;enthalpy is only a function of temperature, hence [tex]c_p[/tex]T = h

where;

[tex]h_1[/tex] is the specific enthalpy at inlet  = [tex]c_pT_1[/tex]

[tex]h_2[/tex] is the specific enthalpy at  outlet = [tex]c_pT_2[/tex]

[tex]c_p[/tex]  = 1.004  kJ/kg.K or 1004 J/kg.K

Given that:

[tex]T_1[/tex] (K) = 249

[tex]V_1[/tex] (m/s) = 209

∴

[tex]h_2=C_pT_1+ \dfrac{V_1^2}{2}[/tex]

[tex]h_2=1004 \times 249+ \dfrac{209^2}{2}[/tex]

[tex]h_2 = 249996+21840.5[/tex]

[tex]\mathbf{\mathtt{h_2 = 271836.5 \ J/kg}}[/tex]

[tex]\mathbf{h_2 = 271.84 \ kJ/kg}}[/tex]

Determine the temperature (K) at state 2.

SInce; [tex]\mathtt{h_2 = c_pT_2 = 271.84 \ kJ/kg}[/tex]

[tex]\mathtt{ c_pT_2 = 271.84 \ kJ/kg}[/tex]

[tex]\mathtt{T_2 = \dfrac{271.84 \ kJ/kg}{ c_p}}[/tex]

[tex]\mathtt{T_2 = \dfrac{271.84 \ kJ/kg}{1.004 \ kJ/kg.K}}[/tex]

[tex]\mathbf{T_2 =270.76 \ K}}[/tex]

Determine the pressure (kPa) at state 2.

For isentropic condition,

[tex]\mathtt{ \dfrac{T_2}{T_1}= \begin {pmatrix} \dfrac{p_2}{p_1} \end {pmatrix} ^\dfrac{k-1}{k}}[/tex]

where ;

k = specific heat ratio = 1.4

[tex]\mathtt{ \dfrac{270.76}{249}= \begin {pmatrix} \dfrac{p_2}{61} \end {pmatrix} ^\dfrac{1.4-1}{1.4}}[/tex]

[tex]\mathtt{ 1.087389558= \begin {pmatrix} \dfrac{p_2}{61} \end {pmatrix} ^\dfrac{0.4}{1.4}}[/tex]

[tex]\mathtt{ 1.087389558 \times 61 ^ {^ \dfrac{0.4}{1.4} }}=p_2} ^\dfrac{0.4}{1.4}}[/tex]

[tex]\mathtt{ 3.519487255=p_2} ^\dfrac{0.4}{1.4}}[/tex]

[tex]\mathtt{ \mathbf{ p_2 = \sqrt[0.4]{3.519487255^{1.4}} }}[/tex]

[tex]\mathtt{ \mathbf{ p_2 = 81.79 \ kPa }}[/tex]

d. Determine the temperature (K) at state 3.

For the isentropic process

[tex]\mathtt{\dfrac{T_3}{T_2} = \begin {pmatrix} \dfrac{p_3}{p_2} \end {pmatrix}^{\dfrac{k-1}{k}}}[/tex]

where;

[tex]\mathtt{\dfrac{p_3}{p_2} }[/tex] is the compressor ratio [tex]\mathtt{r_p}[/tex]

Given that ; the compressor ratio [tex]\mathtt{r_p}[/tex] = 10.7

[tex]\mathtt{\dfrac{T_3}{T_2} = \begin {pmatrix} r_p \end {pmatrix}^{\dfrac{k-1}{k}}}[/tex]

[tex]\mathtt{\dfrac{T_3}{270.76} = \begin {pmatrix} 10.7 \end {pmatrix}^{\dfrac{1.4-1}{1.4}}}[/tex]

[tex]\mathtt{\dfrac{T_3}{270.76} = \begin {pmatrix} 10.7 \end {pmatrix}^{^ \dfrac{0.4}{1.4}}}[/tex]

[tex]\mathtt{{T_3}{} =270.76 \times\begin {pmatrix} 10.7 \end {pmatrix}^{^ \dfrac{0.4}{1.4}}}[/tex]

[tex]\mathbf{ T_3 = 532.959 \ K}[/tex]

Answer:

The answers to your questions are given below.

Explanation:

The following data were obtained from the question:

Red (R) = 4

White (W) = 7

1. Determination of the sample space, S.

The box contains 4 red balls and 7 white balls. Therefore, the sample space (S) can be written as follow:

S = {R, R, R, R, W, W, W, W, W, W, W}

nS = 11

2. Determination of the probability of all results that appeared in the sample space.

From the question, we were told that the two balls was drawn with return. There, the probability of all results that appeared in the sample space can be given as follow:

i. Probability that the first draw is red and the second is also red.

P(R1) = nR/nS

Red (R) = 4

Space space (S) = 11

P(R1) = nR/nS

P(R1) = 4/11

P(R2) = nR/nS

P(R2) = 4/11

P(R1R2) = P(R1) x P(R2)

P(R1R2) = 4/11 x 4/11

P(R1R2) = 16/121

Therefore, the Probability that the first draw is red and the second is also red is 16/121.

ii. Probability that the first draw is red and the second is white.

Red (R) = 4

White (W) = 7

Space space (S) = 11

P(R) = nR/nS

P(R) = 4/11

P(W) = nW/nS

P(W) = 7/11

P(RW) = P(R) x P(W)

P(RW) = 4/11 x 7/11

P(RW) = 28/121

Therefore, the probability that the first draw is red and the second is white is 28/121.

iii. Probability that the first draw is white and the second is also white.

White (W) = 7

Space space (S) = 11

P(W1) = nW/nS

P(W1) = 7/11

P(W2) = nW/n/S

P(W2) = 7/11

P(W1W2) = P(W1) x P(W2)

P(W1W2) = 7/11 x 7/11

P(W1W2) = 49/121

Therefore, the probability that the first draw is white and the second is also white is 49/121.

iv. Probability that the first draw is white and the second is red.

Red (R) = 4

White (W) = 7

Space space (S) = 11

P(W) = nW/nS

P(W) = 7/11

P(R) = nR/nS

P(R) = 4/11

P(WR) = P(W) x P(R)

P(WR) = 7/11 x 4/11

P(WR) = 28/121

Therefore, the probability that the first draw is white and the second is red is 28/121.

Answer: y' = - x'

Explanation:

Let f(x) = 2x + y

then f'(x) = 2 + y'

Let f(y) = x - 2y

then f'(y) = x' - 2

Given:  f'(x) + f'(y) = 0

         2 + y' + x' - 2 = 0

                y' + x'= 0

                 y' = -x'

This can also be written as:       [tex]\dfrac{dy}{dx}=-\dfrac{d}{dx}[/tex]

Answer: hello attached below is the diagram which is part of your question

Total entropy change  = entropy change in cold reservoir + entropy change in hot reservoir = -0.166 + 0.083 = -0.0837 kj/k  it violates Clausius increase of entropy which is Sgen > 0

Explanation:

Clausius statement states that it is impossible to transfer heat energy from a cooler body to a hotter body in a cycle or region without any other external factors affecting it .  

applying the increase in entropy principle to prove this

temp of cold reservoir (t hot)= 600 k

temp of hot reservoir(t cold) = 1220 k

energy (q) = 100 kj

total entropy change  = entropy change in cold reservoir + entropy change in hot reservoir = -0.166 + 0.083 = -0.0837 kj/k

entropy change in cold reservoir = Q/t cold = 100 / 600 = -0.166 kj/k

entropy change in hot reservoir = Q / t hot = 100 / 1220 = 0.083 kj/k

hence it violates  Clausius inequality of increase of entropy principle which is states that generated entropy has to be > 0

Answer:

  leakage

Explanation:

That current is "leakage current."

Answer: A prototype

Explanation:

The scale model that proves the initial concept is called a domain model.

A copy or depiction of something where all parts have the same dimensions as the original. A scale model is an image or copy of an object that is either larger or smaller than the object being represented's actual size.

A domain model is a type of conceptual model that is used to depict the structural elements and conceptual constraints within a domain of interest.

A domain model will include all of the entities, their attributes, and relationships, as well as the constraints that govern the conceptual integrity of the structural model elements that comprise that problem domain.

Therefore, a domain model is the scale model that proves the initial concept.

To learn more about the scale model, refer to the below link:

https://brainly.com/question/14341149

#SPJ2

Answer:

a) Mt = 0.0023229

b) = U1 = 214.07

c) = V₁  = 0.861 m³/kg

d) = Vr1 = 621.2

Explanation:

Given that

R = 0.287 KJ/kg.K, T1 = 300 K , P1 = 100 kPa , V1 = 500 cm³, r = 10 , Q = 60 kW , Speed N = 5600 RPM, Number of cylinders K = 4

specific heat at constant volume Cv = 0.7174 kJ/kg.K

Specific heat at constant pressure is 1.0045 Kj/kg.K

a)  To determine the total mass (kg) of air in the engine.

we say

P1V1 = mRT1

we the figures substitute

(100 x 10³) ( 500 x  10⁻⁶) = m ( 0.287 x  10³) ( 300 )

50 = m x 86100

m = 0.00005 / 86100 = 0.0005807 ( mass of one cylinder)

Total mass of 4 cylinder

Mt = m x k

Mt = 0.0005807 x 4

Mt = 0.0023229

b) To determine the specific internal energy (kJ/kg) at state 1

i.e at T1 = 300

we obtain the value of specific internal energy U1 at 300 K ( state 1) from the table ideal gas properties of air.

U1 = 214.07

c) To determine the specific volume (m³/kg) at state 1.

we say

V₁ = V1/m

V₁ = (500 x  10⁻⁶) / 0.0005807

V₁  = 0.861 m³/kg

d) To determine the relative specific volume at state 1.

To obtain the value of relative specific volume at 300 K ( i.e state 1) from the table ideal gas properties of air.

At T1 = 300 k

Vr1 = 621.2

I inferred you want literal editing of the text above.

Explanation:

Here's a correction of the sentences:

1. The author, an expert in cybersecurity will speak via Zoom on Wednesday.

In this sentence, punctuation mark ( , ) was added and the word  'this' was replaced with 'on'.

2. Williams' book contains many illustrations, which makes it easy to read.

Added punctuation and made a revision of the sentence.

3. Based on the available evidence, the university administrators have opted for a hybrid format for the fall, which begins September 20.

Mainly added punctuations to make the senstence clarer.

4. (Thesis statement) I believe Free laptops should be offered to all students who need them.

Made a few additions.

Answer:

Explanation:

In a particular application involving airflow over a heated surface, the boundary layer temperature distribution, T(y), may be approximated as:

[ T(y) - Ts / T∞ - Ts ] = 1 - e^( -Pr (U∞y / v) )

where y is the distance normal to the surface and the Prandtl number, Pr = Cpu/k = 0.7, is a dimensionless fluid property. a.) If T∞ = 380 K, Ts = 320 K, and U∞/v = 3600 m-1, what is the surface heat flux? Is this into or out of the wall? (~-5000 W/m2 , ?). b.) Plot the temperature distribution for y = 0 to y = 0.002 m. Set the axes ranges from 380 to 320 for temperature and from 0 to 0.002 m for y. Be sure to evaluate properties at the film temperature.

Answer:

a) the minimum time (minutes) for the aluminium casting to solidify is 2.86 min

b) the minimum time (minutes) for the grey iron casting to solidify is 2.13 min. Therefore solidification of grey iron cast will take less time (2.13 min) compared to the solidification of the aluminium cast (2.86 min)

Explanation:

Given that; diameter of Disk = 500 mm, thickness t = 20, mold constant Cm = 2.0 sec/mm²

first we find the volume and Area;

Volume V = πD²t / 4

Volume V = π × (500)² × 20 / 4 = 3,926,991 mm³

Area A = 2πD²/ 4 + πDt

Area A = {[π × (500)²] / 2} +{ π × (500) × (20)}

Area A = 392,699.08 + 31,415.93

Area A = 424,115 mm²

a)

Chvorinov’s rule

T(aluminium) = Cm (V/A) ²

T(aluminium) =  2.0 × (3,926,991 / 424,115) ²

T(aluminium) = 171.5 s = 2.86 min

∴ the minimum time (minutes) for the casting to solidify is 2.86 min

b)

For cast iron

Cm (mold constant = 1.488 sec/mm²)

Chvorinov’s rule

T(iron) = Cm (V/A) ²

T(iron) = 1.488 × (3,926,991 / 424,115) ²

T(iron) = 127.5720s = 2.13 min

Therefore solidification of grey iron cast will take less time (2.13 min) compared to the solidification of the aluminium cast (2.86 min)

Answer:

efficiency

Explanation:

Answer:

The correct answer is Efficiency.

Explanation:

I got it right on the plato test.

Answer:

load speeds:

For V = 100 v  speed = 188 rad/sec

For V = 75 v   speed = 138 rad/sec

For V = 50 v   speed = 88 rad/sec

Explanation:

Given data

Ra = 0.3 Ω

Ke = Kt = 0.5

torque = 10 Nm

using  a constant torque = 10 Nm we can calculate the various load speed for the given values of 100 v , 75 v, 50 v

attached below is the detailed solutions and plot

Answer:

True

Explanation:

I looked it up

Answer:

true

Explanation:

Answer:

A) 251.8 kj/kg

B) 0.9150 kj/kg-k

C) 155.4 kj/kg

F) 1.50

G) 3.95 kw

H) 2.6 kw

Explanation:

Given conditions :

air conditioner : R -134a

compressor efficiency (nc) = 90%.

T1 = 9⁰c,  T3 = 39⁰c, mass flow rate = 0.027 kg/s

A) Specific enthalpy at the compressor inlet

at T = 9⁰c the saturated vapor (x) = 1

from the R-134a property table

h1 = 251.8 kj/kg

B ) specific entropy ( kj/kg-k) at the compressor inlet

at T = 9⁰c the saturated vapor (x) = 1

s = 0.9150 kj/kg-k ( from the R-134a property table )

C) specific enthalpy at the compressor exit

at T3 = 39⁰c , s2 = s1

has = 165.12 kj/kg

h2 = 155.4 kj/kg

attached below is the remaining solution to some of the problems

Answer:

pay off the parking tickets

Explanation:

In the scenario being described, the best thing to do would be to pay off the parking tickets. The parking tickets stay under your name, and if they are not paid in time can cause problems down the road. For starters, if they are not paid in time the amount will increase largely which will be harder to pay. If that increased amount is also not paid, then the government will suspend your licence indefinitely which can later lead to higher insurance rates.

Answer:

The answer is below

Explanation:

An AC voltage is represented by the relation v= 12 sin(500πt). Determine the:

The equation of an AC voltage is given as:

[tex]V=V_msin(2\pi ft)[/tex]

Where Vm is the maximum value of voltage and f is the frequency

From V= 12 sin(500πt), Vm = 12, 2πft = 500πt

(a) The peak to peak voltage is total amplitude (both the negative and positive amplitude) of the voltage, it is the difference between the positive amplitude and the negative amplitude. The peak to peak voltage ([tex]V{p-p}[/tex]) is given as:

[tex]V_{p-p}=2V_m=2*12=24\ V[/tex]

b) The frequency is the number of oscillation per second. The frequency (f) is gotten from:

2πft = 500πt

2f = 500

f = 500/2

f = 250 Hz

c) The root mean square voltage is the dc value of the voltage. It is given by:

[tex]V_{rms}=\frac{V_m}{\sqrt{2} }=\frac{12}{\sqrt{2} }=8.5\ V[/tex]

d) The period (T) is the time taken to complete one oscillation, it is given by:

[tex]T=\frac{1}{f}\\ \\T=\frac{1}{250} =0.004\ s[/tex]

Answer:

b. inversely proportional to radius of curvature

Explanation:

In curvilinear motions, the normal acceleration which is also called the centripetal acceleration is always directed towards the center of the circular path of motion. This acceleration has a magnitude that is directly proportional to the square of the speed of the body undergoing the motion and inversely proportional to the radius of the curvature of the motion path. The centripetal or normal acceleration a,  can be given by;

a = [tex]\frac{v^2}{r}[/tex]

Where;

v = speed of the body

r = radius of curvature.

Answer:

True

Explanation:

Bona Fide is a Latin term which means in good faith or without any intention to deceive. The business established on a bona fide basis means that there is an absence of fraud. The marketing agency has devoted its services to public relations, advertising and promoting the services of clients. There is no intention of fraud in the business.

Answer:

b. What is the operator's efficiency for the day?

                                                      AND

e. What would be the proper piece rate (rate expressed in money) for this job, assuming that the above time standard is correct?

Explanation:

Answer:

the torque required to RAISE the load is Tr = 18.09 Nm

the torque required to LOWER the load is Tl = 10.069 ≈ 10.07 Nm

the Overall Efficiency e = 0.2199 ≈ 0.22

Explanation:

Given that; F = 5 kN, p = 5mm, d = 35mm

Dm = d - p/2

Dm = 35 - ( 5/2) = 35 - 2.5

DM = 32.5mm

So the torque required to RAISE the load is

Tr = ( 5 × 32.5)/2 [(5 + (π × 0.09 × 32.5)) / ( (π × 32.5) - ( 0.09 × 5))] + [( 5 × 0.06 × 45)/2]

Tr = 81.25 × (14.1892 / 101.6518) + 6.75

Tr = 11.3414 + 6.75

Tr = 18.09 Nm

the torque required to LOWER the load is

Tl =  ( 5 × 32.5)/2 [(π × 0.09 × 32.5) - 5) / ( (π × 32.5) + ( 0.09 × 5))] + [( 5 × 0.06 × 45)/2]

Tl = 81.25 × 4.1892 / 102.5518 + 6.75

Tl = 3.3190 + 6.75

Tl = 10.069 ≈ 10.07 Nm

So since torque required to LOWER the load is positive

that is, the thread is self locking

Therefore the efficiency is

e = ( 5 × 5 ) / ( 2π × 18.09 )

e = 25 / 113.6628

e = 0.2199 ≈ 0.22

Answer:

30 feet

Explanation:

Given data :

design speed = 30 miles/h

super elevation = 0.08

determine the width of the turning roadway

calculate the value of R = V^2 / 15( e + p)

e = 0.08 , p = 0.2 , v = 30

R = (30)^2 / 15 ( 0.08 + 0.2 )

  = 900 / 15 ( 0.28 )

  ≈ 215 ft

pavement width from the calculation above = 28 ft

width of the turning roadway = pavement width + 2 = 30 feet ( because there are two vertical widths joining up the main road at the T junction )

Answer: answer provided in the explanation section.

Explanation:

Weather phenomenons that would impart Aviation Operations in Santa Barbara -

1. Although winters are cold, wet, and partly cloudy here. It is in general favorable for flying. But sometimes strong winds damage this pleasant weather.

2.  The Sundowner winds cause rapid warming and a decrease in relative humidity. The wind speed is very high surrounding this area for this type of wind.  

3. Cloud is an important factor that affects aviation operations. Starting from April, here the sky is clouded up to November. The sky is overcast (80 to 100 percent cloud cover) or mostly cloudy (60 to 80 percent) 44% on a yearly basis. Thus extra cloud cover can trouble aviation operations.

4. The average hourly wind speed can also be a factor. This also experiences seasonal variations, these variations are studied carefully in the aviation industry. The windier part of the year starts in January and ends in June. In April, the wind speed can reach 9.5 miles per hour.

This and more are some factors to look into when considering wheather conditions that would affect aviation operations.

I hope this was a bit helpful. cheers

Answer:

moment of inertia = 4.662 * 10^6 [tex]mm^4[/tex]

Explanation:

Given data :

Mass of machine = 400 kg = 400 * 9.81 = 3924 N

length of span = 3.2 m

E = 200 * 10^9 N/m^2

frequency = 9.3 Hz

Wm ( angular frequency ) = 2 [tex]\pi f[/tex] = 58.434 rad/secs

also Wm = [tex]\sqrt{\frac{g}{t} }[/tex]  ------- EQUATION 1

g = 9.81

deflection of simply supported beam

t = [tex]\frac{wl^3}{48EI}[/tex]

insert the value of t into equation 1

W[tex]m^2[/tex] = [tex]\frac{g*48*E*I}{WL^3}[/tex]   make I the subject of the equation

I ( Moment of inertia about the neutral axis ) = [tex]\frac{WL^3* Wn^2}{48*g*E}[/tex]

I = [tex]\frac{3924*3.2^3*58.434^2}{48*9.81*200*10^9}[/tex]  = 4.662 * 10^6 [tex]mm^4[/tex]

Answer: Tl = - 13.3°C

the lowest outdoor temperature is - 13.3°C

Explanation:

Given that;

Temperature of Th = 21°C = 21 + 273 = 294 K

the rate at which heat lost is Qh = 5400 kJ/h°C

the power input to heat pump Wnet = 6 kw

The COP of a reversible heat pump depends on the temperature limits in the cycle only, and is determined by;

COPhp = Th/(Th - Tl)

COPhp = Qh/Wnet

Qh/Wnet = Th/(Th -Tl)

the amount of heat loss is expressed as

Qh = 5400/3600(294 - Tl)

the temperature of sink

( 5400/3600(294 - Tl)) / 6 = 294 / ( 294 - Tl)

now solving the equation

Tl = 259.7 - 273

Tl = - 13.3°C

so the lowest outdoor temperature is - 13.3°C

Answer:

d. all of the above

Explanation:

There are two components of acceleration for a particle moving in a circular path, radial and tangential acceleration.

The radial acceleration is given by;

[tex]a_r = \frac{V^2}{R}[/tex]

Where;

V is the velocity of the particle

R is the radius of the circular path

This radial acceleration is always directed towards the center of the path, perpendicular to the tangential acceleration and negative.

Therefore, from the given options in the question, all the options are correct.

d. all of the above

There are different type of acceleration.  The radial component of acceleration of a particle moving in a circular path is always negative, directed towards the center of the path and perpendicular to the transverse component of acceleration.

This is due to because of the centripetal force. So centripetal force is the reason for a radial acceleration.

Learn more from

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Answer:

D) is due to an increase of the armature current.

Explanation:

Option D is correct because on the DC motor, when the load increases, it leads to an increase in the armature current.

The armature current then sets up a magnetic flux which opposes the main field flux. The net field flux gets reduced. It is at this point, the armature reaction occurs.

Armature reaction is seen as the effect of magnetic flux which is usually set up by an armature current. This occurs when there is the distribution of flux under the main poles.

There are two effects the armature flux causes on the main field flux.

1. The main field flux is distorted by the armature reaction.

2. The magnitude of the main field flux is reduced by the armature flux.

Answer:

Average heat transfer coefficient =  31 kw/m^2 k

Heat transfer rate per meter length of pipe =  116.808 KW

Explanation:

water temperature = 20⁰c,  

free-stream velocity = 1.5 m/s

circular pipe diameter = 2.0 cm = 0.02 m

surface temperature = 80⁰c

A) calculate average heat transfer coefficient

we apply the formula below :

m = αAv

A (area) = [tex]\pi /4 (d)^2[/tex]

m = 10^3 * [tex]\pi / 4 ( 0.02)^2[/tex] * 1.5

   = 10^3 * 0.7857( 0.0004) * 1.5

   = 0.4714 kg/s

Average heat transfer coefficient  

h = [tex]\frac{m(cp)}{A}[/tex]  ,  A = [tex]\pi DL[/tex]

L = 1 m , m = 0.4714 kgs , cp = 4.18

back to equation

h = [tex]\frac{0.4714*4.18}{\pi * 0.02 }[/tex]   = 1.970 / 0.0628 = 31.369 ≈ 31 kw/m^2 k

B) Heat transfer rate per meter length of pipe

Q = ha( ΔT ),  a = [tex]\pi DL[/tex]

   = 31 * 0.0628 * ( 80 - 20 )

  = 31 * 0.0628 * 60 = 116.808 KW

Answer:

the rate of heat loss from the duct to the attic space = 1315.44 W

the pressure difference between the inlet and outlet sections of the duct  = 7.0045 N/m²

Explanation:

We know that properties of air 80⁰C  and 1atm  (from appendix table) are;

density p = 0.9994 kg/m³, Specifice heat Cp = 1008 J/kg.⁰C

Thermal conductivity k = 0.02953 W/m.⁰C, Prandtl number Pr = 0.7154,

Kinematic viscosity v = 2.097 × 10⁻⁵ m²/s

haven gotten that, we calculate the hydraulic diameter of square duct

Dh = 4Ac / P      { Ac = is cross sectional area of duct and P = perimeter}

now we substitute a² for Ac and 4a for P ( we know from the question that a = 0.2 m)

Dh = 4a² / 4a

Dh = 4(0.2)² / 4(0.2)

Dh = 0.2 m

Now we calculate the average velocity of air

Vₐ = Vˣ / Ac        { vˣ = volume flow rate of air}

Vₐ = Vˣ / a²      { Ac = a² }, we know that a = 0.2m₂, Vˣ = 0.15 m³

Vₐ = 0.15 / (0.2)²

Vₐ = 3.75 m/s

Next we calculate the Reynolds number

Re = Vₐ Dh / V

Re = (3.75 × 0.2) / 2.097× 10⁻⁵

Re = 35765.379

The  Reynolds number IS GREATER than 10,000

so the flow is turbulent and entry length in this case is nearly 10 times the hydraulic diameter

Lh ≈ Lt ≈ 10D

= 10 × 0.2

= 2m

As this length is quite small when compared to the total of tube, we assume fully developed flow for the entire tube length.

Now we calculate the Nusselt number from this relation;

Nu =  0.023 Re⁰'⁸ Pr⁰'³

so we substitute for Re and Pr

Nu = 0.023(35765.379)⁰'⁸ (0.7154)⁰'³

Nu = 91.4

Now calculate the convective heat transfer coefficient

h = Nu × K/ Dh

we substitute

h = 91.4 × 0.02953 W/m.°C / 0.2 m

h = 13.5 W/m².°C

We calculate the surface area of the square duct

Aₓ = 4aL       { L= length of duct}

we substitute

Aₓ = 4 × 0.2 × 8

Aₓ = 6.4 m²

Mass flow rate of air

m = pVˣ

we substitute again ( from our initials)

m = 0.9994 kg/m₃ × 0.15 m³/s

m= 0.150 kg/s

We calculate the exit temperature of the air from the duct

Te = Ts - (Ts -Ti) exp ( - hAₓ / mCp)

we know that

Ts = 60°C , Ti = 80°C, h = 13.5 W/m².°C , Aₓ = 6.4m², m = 0.150 kg/s , Cp = 1008 J/kg.°C

we substitute

Te = 60 - (60-80) exp(- ((13.5 × 6.4)/(0.15 × 1008))

Te = 71.3°

Now we calculate the rate of heat loss from the duct.

Q = mCp ( Ti -Te )

we substitute again

Q = 0.150 × 1008 × ( 80 - 71.3 )

Q = 1315.44 W

Next we calculate the estimated friction factors by using Haaland equation

1/√f = - 1.8log₁₀ [ 6.9/Re + (E/D)/3.7)¹'¹¹]

we know that E/D = relative roughness = 10⁻³

we substitute

so

1/√f = - 1.8log₁₀ [ (6.9/35765.379) + ( 10⁻³/3.7)¹'¹¹]

1/√f = - 1.8log₁₀ { 0.000192924 + 0.00010947}

1/√f = - 1.8log₁₀ 0.000302324  

√f =   1/6.334

f = (1/6.334)²

f = 0.02492

We calculate the pressure difference between inlet and outlet sections of the duct

ΔPl = fLPVa² / Dh × 2

ΔPl = {0.02492 × 8 × 0.9994 × (3.75)²} / 0.2 × 2

ΔPl = 2.8018 / 0.4

ΔPl = 7.0045 N/m²

Therefore pressure deference is 7.0045 N/m²