Explanation Given information: The stagnation pressure for incompressible flow is defined as, p 0 = p + 1 2 ρ V 2 The binomial series is defined as, ( 1 + x ) α = 1 + α x + α ( α − 1 ) 2 ! x 2 + α ( α − 1 ) ( α − 2 ) 3 ! x 3 + ...... For an ideal gas isentropic flow, The pressure ratio is defined as, p 0 p = [ 1 + 1 2 ( k − 1 ) M a 2 ] k / k − 1 Calculation: According to the above explanation, The binomial series expansion for pressure ration equation will be, p 0 p = [ 1 + 1 2 ( k − 1 ) M a 2 ] k / k − 1 = 1 + 1 2 ( k k − 1 ) ( k − 1 ) M a 2 + 1 2 ( k k − 1 ) ( k k − 1 − 1 ) ( 1 2 ( k − 1 ) M a 2 ) 2 + 1 6 ( k k − 1 ) ( k k − 1 − 1 ) ( k k − 1 − 2 ) ( 1 2 ( k − 1 ) M a 2 ) 3 + To determine (b) To find: the Mach number where the error is equal to 4 % .

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 9, Problem 9.24P

To determine

(a)

To show: that the isentropic relation can be expanded as,

p0≈p+12ρV2(1+14Ma2+2−k24Ma4+....).

To determine

(b)

To find: the Mach number where the error is equal to 4%.

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Chapter 9, Problem 9.23P

Chapter 9, Problem 9.25P

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Chapter 9 Solutions

Fluid Mechanics

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(a) To show: that the isentropic relation can be expanded as, p 0 ≈ p + 1 2 ρ V 2 ( 1 + 1 4 M a 2 + 2 − k 24 M a 4 + .... ) .

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(a) To show: that the isentropic relation can be expanded as, p0≈p+12ρV2(1+14Ma2+2−k24Ma4+....).

(b) To find: the Mach number where the error is equal to 4%.

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Chapter 9 Solutions

(a)

To show: that the isentropic relation can be expanded as,

p0≈p+12ρV2(1+14Ma2+2−k24Ma4+....).

(b)

To find: the Mach number where the error is equal to 4%.