Determine the Mach number of a car moving in standard air at a speed of (a) \(25 \mathrm{mph}\) (b) \(55 \mathrm{mph},\) and (c) \(100 \mathrm{mph}\)

Short Answer

Expert verified
The Mach numbers for these speeds are: a) Approximately 0.03 for 25 mph, b) Approximately 0.07 for 55 mph, c) Approximately 0.13 for 100 mph.

Step by step solution

01

Conversion of Speed of Sound into mph

Firstly, it is needed to have the speed of sound in the same units as those of the speeds given, which are in miles per hour (mph). The speed of sound in standard air under normal conditions is approximately 343 m/s. To convert 343 m/s to mph, use the conversion factor 1 m/s = 2.237 mph. Therefore, \(343 \, m/s \times 2.237 \, mph/(m/s) = 767 \, mph\). So, the speed of sound under the given conditions is 767 mph.
02

Calculation of the Mach Number for 25 mph

The formula to determine the Mach number (M) is \(M = V/a\), where V is the speed of the object and a is the speed of sound in the given medium. Now, substitute the respective values into the formula to calculate the Mach number for a speed of 25 mph: \( M = 25 \, mph / 767 \, mph = 0.0326 \). Thus, the Mach number for a speed of 25 mph is approximately 0.03.
03

Calculation of the Mach Number for 55 mph

Similarly, using the formula from step 2, calculate the Mach number for a speed of 55 mph: \( M = 55 \, mph / 767 \, mph = 0.0717\). Thus, the Mach number for a speed of 55 mph is approximately 0.07.
04

Calculation of the Mach Number for 100 mph

Finally, calculate the Mach number for a speed of 100 mph by substituting the known values into the formula: \(M = 100 \, mph / 767 \, mph = 0.1304\). Thus, the Mach number for a speed of 100 mph is approximately 0.13.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Air is stored in a tank where the pressure is 40 psia and the temperature is \(500^{\circ} \mathrm{R}\). A converging-diverging nozzle with an exitto-throat area ratio of 2.5 attaches the tank to a duct where heat is exchanged with the air. The exit pressure is 15 psia and a normal shock stands at the exit of the nozzle. Determine the magnitude and direction of the heat exchange.

Air flows isentropically through a duct to a section where \(p_{1}=25 \mathrm{kPa}, T_{1}=300 \mathrm{K},\) and \(V_{1}=900 \mathrm{m} / \mathrm{s} .\) For these conditions: (a) Determine the stagnation conditions for the flow. (b) What is the Mach number at station \(1 ?\) Show a \(T-s\) diagram displaying stagnation and static conditions. (c) Is the flow choked? Is the throat behind or ahead of section \(1 ?\) Label this state on the \(T-s\) diagram.

The static pressure to stagnation pressure ratio at a point in a gas flow field is measured with a Pitot-static probe as being equal to \(0.6 .\) The stagnation temperature of the gas is \(20^{\circ} \mathrm{C}\). Determine the flow speed in \(\mathrm{m} / \mathrm{s}\) and the Mach number if the gas is air. What error would be associated with assuming that the flow is incompressible?

The gas entering a rocket nozzle has a stagnation pressure of \(1500 \mathrm{kPa}\) and a stagnation temperature of \(3000^{\circ} \mathrm{C}\). The rocket is traveling in the still Standard Atmosphere at \(30,000 \mathrm{m}\). Find the throat and exit area for a flow rate of \(10 \mathrm{kg} / \mathrm{s}\). Assume \(k=1.35, R=\) \(287.0 \mathrm{N} \cdot \mathrm{m} / \mathrm{kg} \cdot \mathrm{K} .\) The gas is perfectly, expanded to the ambient pressure.

A nozzle for a supersonic wind tunnel is designed to achieve a Mach number of \(3.0,\) with a velocity of \(2000 \mathrm{m} / \mathrm{s},\) and a density of \(1.0 \mathrm{kg} / \mathrm{m}^{3}\) in the test section. Find the temperature and pressure in the test section and the upstream stagnation conditions. The fluid is helium.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free