5. Use dimensional analysis to estimate quantities. Consider a gas with density p, pressure p, and ratio of specific heats y. The speed of sound, c, is an important parameter when considering high-speed gaseous flows where compressibility of the gas may be significant (planes, turbines, etc.). (a) Use dimensional analysis to derive a formula for the speed of sound, c = f(y, p,p). (Recall that dimensional analysis can't give you the *exact* relationship between dimensionless groups, so you might need to guess how c varies with y.) (b) Look up the density of air at 25° C at ambient pressure. Assume you don't know y- let's say y = 1 as a guess. Use your formula to estimate what c is, in meters per second. How close (or far) is your estimate from the experimentally determined value (346.1 m/s), in terms of % error? (c) Use your formula from part (a) to determine the ratio of the speed of sound through helium compared to air. Why do people sound funny after they breathe in helium?

5. Use dimensional analysis to estimate quantities. Consider a gas with density p, pressure p, and ratio of specific heats y. The speed of sound, c, is an important parameter when considering high-speed gaseous flows where compressibility of the gas may be significant (planes, turbines, etc.). (a) Use dimensional analysis to derive a formula for the speed of sound, c = f(y, p,p). (Recall that dimensional analysis can't give you the exact relationship between dimensionless groups, so you might need to guess how c varies with y.) (b) Look up the density of air at 25° C at ambient pressure. Assume you don't know y- let's say y = 1 as a guess. Use your formula to estimate what c is, in meters per second. How close (or far) is your estimate from the experimentally determined value (346.1 m/s), in terms of % error? (c) Use your formula from part (a) to determine the ratio of the speed of sound through helium compared to air. Why do people sound funny after they breathe in helium?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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