Semi-angle of a Mach cone is (a) sin^-1((1)/(√(M))) (b) sin^-1 M (c) sin^-1((1)/(M)) (d) cos^-1(

Name: Problem 31, Chapter 6: Thermal Engineering
Uploaded: 2021-11-25T20:10:01-08:00
Duration: 1 min 3 s
Channel: Hunza Gilgit
Description: Semi-angle of a Mach cone is (a) sin^-1((1)/(√(M))) (b) sin^-1 M (c) sin^-1((1)/(M)) (d) cos^-1((1)/(M)) where M is the Mach number.

step 1 Dear students, in the given multiple choice question MCQs we have asked that the semi angle of m

Question

Semi-angle of a Mach cone is (a) $\sin ^{-1}\left(\frac{1}{\sqrt{M}}\right)$ (b) $\sin ^{-1} \mathrm{M}$ (c) $\sin ^{-1}\left(\frac{1}{\mathrm{M}}\right)$ (d) $\cos ^{-1}\left(\frac{1}{\mathrm{M}}\right)$ where $\mathrm{M}$ is the Mach number.

   Semi-angle of a Mach cone is
(a) $\sin ^{-1}\left(\frac{1}{\sqrt{M}}\right)$
(b) $\sin ^{-1} \mathrm{M}$
(c) $\sin ^{-1}\left(\frac{1}{\mathrm{M}}\right)$
(d) $\cos ^{-1}\left(\frac{1}{\mathrm{M}}\right)$
where $\mathrm{M}$ is the Mach number.

Thermal Engineering

TSadhu Singh,… 1st Edition

Chapter 6, Problem 31

Instant Answer

Solved by Expert Hunza Gilgit

11/25/2021

Step 1

The Mach number (M) is the ratio of the speed of the object to the speed of sound in the fluid. Show more…

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Semi-angle of a Mach cone is (a) $\sin ^{-1}\left(\frac{1}{\sqrt{M}}\right)$ (b) $\sin ^{-1} \mathrm{M}$ (c) $\sin ^{-1}\left(\frac{1}{\mathrm{M}}\right)$ (d) $\cos ^{-1}\left(\frac{1}{\mathrm{M}}\right)$ where $\mathrm{M}$ is the Mach number.

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Key Concepts

Mach Number

The Mach number is the ratio of the velocity of an object moving through a fluid to the speed of sound in that fluid. It is a dimensionless quantity that indicates whether the flow is subsonic, transonic, or supersonic. A Mach number greater than one signifies supersonic speeds, which is a key condition for phenomena like the formation of shock waves and Mach cones.

Mach Cone

A Mach cone is the conical shock wave produced by an object moving at supersonic speeds. Its semi-angle, which is the angle between the direction of motion and the shock wave, is determined by the Mach number. The relationship is given by the inverse sine function, specifically sin?¹(1/M), which defines how the cone narrows as the object's speed increases relative to the speed of sound.

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