Experimental aircraft for the military are to be ranked relative to their Mach number, Ma....

Experimental aircraft for the military are to be ranked relative to their Mach number, Ma. Mach number is a ratio of the velocity, V, of the aircraft to the speed of sound, c. The speed of sound, however, is a function of temperature. The theoretical equations for the speed of sound can be expressed as c = (kRT)0.5, where

k = specific heat ratio that varies with temperature but has no dimension. However, for this problem assume that it is a constant with a value of 1.4.

R = Gas constant for air (53.33 ft · lbf/lbm · °R)

T = Temperature, °R

Let us imagine that we did not know the equation for the speed of sound but had access to data relating the speed of sound in air to temperature. That set of data is recorded in the table below.

(a) Develop a table using spreadsheet software that will provide the necessary variables for Eqs. (10.16), (10.17), and (10.19).

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From the data in part (a) above and the equations presented in the chapter material, determine:

(b) The equation of the line c = bT m

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(c) The coefficient of correlation

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(d) Using the spreadsheet package, determine the equation of the line and the coefficient of determination.

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(e) Does the equation obtained from the data verify the theoretical equation presented for the speed of sound?

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(f) What is the numerical value and what are the units on the constant b? Recall

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(g) Three aircraft were measured at the following velocities and temperatures. Determine the Mach number for each from the equation of the curve in part (b):

1. X101 855 mph at −100 degrees Fahrenheit

2. X215 548 m/s at −95 degrees Celsius

3. X912 2 120 ft/s at 520 degrees Rankine

Speed (ft/s)	Temperature Rankine	Speed (ft/s)	Temperature Rankine
1 00	490	550	1149
1 50	600	600	1201
200	693	650	1250
250	775	700	1297
300	849	750	1342
350	917	800	1387
400	980	850	1429
450	1040	900	1471
500	1096	950	1511
		1 000	1 550