Explanation Given information: The compressible stream function is defined as ρ u = ( ∂ ψ p ∂ y ) and ρ u = − ( ∂ ψ p ∂ x ) . Write the expression for the stream function ψ p in x direction. ρ u = − ∂ ( ψ p ) ∂ x ∂ ( ψ p ) = ρ u ⋅ ∂ x ....... (I) Here, the velocity component in x direction is u , the density of the substance is ρ , the change in the distance in the x direction is ∂ x and the change the stream function ψ p in x direction is ∂ ( ψ p ) . Write the expression for the stream function ψ p in y direction. ρ u = − ∂ ( ψ p ) ∂ y ∂ ( ψ p ) = ρ u ⋅ ∂ y ....... (II) Here, the velocity component in y direction is u , the change in the distance in the y direction is ∂ y and the change the stream function ψ p in y direction is ∂ ( ψ p ) . Write the expression for the density. ρ = mass length 3 ....... (III) Write the expression for velocity. u = Length time ....... (IV) Write the expression for the distance. y = Length ....... (V) Calculation: Substitute M for mass and L for Length in Equation (III). ρ = M L 3 ........ (VI) Substitute s for time and L for Length in Equation (IV). u = L T

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259877827

Author: CENGEL

Publisher: MCG

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Chapter 9, Problem 60P

To determine

The units of the stream function in primary Si units and Primary English units.

The unit dimension of the stream function.

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Chapter 9, Problem 59P

Chapter 9, Problem 61P

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Chapter 9 Solutions

Fluid Mechanics: Fundamentals and Applications

Ch. 9 - Explain the fundamental differences between a flow...Ch. 9 - What does it mean when we say that two more...Ch. 9 - The divergence theorem is v.cdv=A c . n dA Ch. 9 - Prob. 4CP Ch. 9 - Prob. 5CP Ch. 9 - Prob. 6CP Ch. 9 - Prob. 7P Ch. 9 - Prob. 8P Ch. 9 - Let vector G=2xzi12x2jz2kk . Calculate the...Ch. 9 - Prob. 10P

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The units of the stream function in primary Si units and Primary English units. The unit dimension of the stream function.