determine the mach number of a car moving in air (at 61of) at a speed of 177 mph (miles-per-hour). note: k for air may be assumed as 1.4; a useful gas constant might be 1716 ft-lb/slug-or.

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Answer 1

The Mach number of the car moving in air at a speed of 177 mph is approximately 2.36.

To determine the Mach number of a car moving in air, we need to calculate the ratio of the car's velocity to the speed of sound.

- Speed of the car: 177 mph (miles per hour)

- Temperature of the air: 61 °F

First, let's convert the car's speed from mph to ft/s:

$$\text{Speed of the car} = 177 \, \text{mph} \times \frac{5280 \, \text{ft}}{1 \, \text{mile}} \times \frac{1 \, \text{hour}}{3600 \, \text{s}}$$

$$\text{Speed of the car} = 258.8 \, \text{ft/s}$$

Next, let's convert the air temperature from °F to °R (Rankine):

$$\text{Temperature of the air} = 61 \, \text{°F} + 459.67 \, \text{°R}$$

$$\text{Temperature of the air} = 520.67 \, \text{°R}$$

Now, let's calculate the speed of sound in the air using the equation:

$$\text{Speed of sound} = \sqrt{\gamma \cdot R \cdot T}$$

- $\gamma$ is the specific heat ratio for air (given as 1.4)

- $R$ is the specific gas constant for air (given as 1716 ft-lb/slug-°R)

- $T$ is the temperature of the air in °R

Substituting the values into the equation:

$$\text{Speed of sound} = \sqrt{1.4 \cdot 1716 \, \text{ft-lb/slug-°R} \cdot 520.67 \, \text{°R}}$$

$$\text{Speed of sound} = \sqrt{12087.288 \, \text{ft²/s²}}$$

$$\text{Speed of sound} = 109.76 \, \text{ft/s}$$

Finally, we can calculate the Mach number using the formula:

$$\text{Mach number} = \frac{\text{Speed of the car}}{\text{Speed of sound}}$$

$$\text{Mach number} = \frac{258.8 \, \text{ft/s}}{109.76 \, \text{ft/s}}$$

$$\text{Mach number} \approx 2.36$$

Thus, the appropriate answer is approximately 2.36.

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Related Questions

a new integration method based on the coupling of mutistage osculating cones waverider and busemann inlet for hypersonic airbreathing vehicles

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Therefore, the phrase describes a new method of integrating multistage osculating cones, waverider, and Busemann inlet technologies to improve the performance of hypersonic airbreathing vehicles. This integration aims to enhance aerodynamic efficiency and reduce drag, ultimately leading to more efficient and faster vehicles.

The phrase "a new integration method based on the coupling of multistage osculating cones waverider and Busemann inlet for hypersonic airbreathing vehicles" refers to a method of combining different technologies to improve the performance of hypersonic airbreathing vehicles. Here is a step-by-step explanation:

1. Multistage osculating cones: These are structures that change shape at different stages of flight to optimize aerodynamic performance. They are used to reduce drag and increase efficiency.

2. Waverider: A waverider is a type of vehicle design that uses the shockwaves generated by its own supersonic flight to create lift. This design allows for increased aerodynamic efficiency at high speeds.

3. Busemann inlet: A Busemann inlet is a type of air intake design that reduces the effects of shockwaves during supersonic flight. It helps to slow down and compress the incoming air, increasing efficiency and reducing drag.

4. Integration method: The integration method mentioned in the question refers to combining the multistage osculating cones, waverider, and Busemann inlet technologies to create a more efficient and high-performing hypersonic airbreathing vehicle.

The phrase describes a new method of integrating multistage osculating cones, waverider, and Busemann inlet technologies to improve the performance of hypersonic airbreathing vehicles. This integration aims to enhance aerodynamic efficiency and reduce drag, ultimately leading to more efficient and faster vehicles.

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