Explanation Write the expression of the velocity component in x axis for two dimensional flow. u = a x + b x x 2 y 2 = a x + b x y 2 (I) Here, the displacement in x axis is x , the displacement in y axis is y and the constants are a and b . Write the expression of the velocity component in y axis for two dimensional flow. v = a y + b y x 2 y 2 = a y + b x 2 y (II) Write the expression of x component of the acceleration. a x = ∂ u ∂ t + u ∂ u ∂ x + v ∂ u ∂ y (III) Differentiate Equation (I) with respect to t on both sides. ∂ u ∂ t = ∂ ∂ t ( a x + b x y 2 ) = ∂ ∂ t ( a x ) + ∂ ∂ t ( b x y 2 ) = 0 Differentiate Equation (I) with respect to x on both sides. ∂ u ∂ x = ∂ ∂ x ( a x + b x y 2 ) = ∂ ∂ x ( a x ) + ∂ ∂ x ( b x y 2 ) = a − b x 2 y 2 Differentiate Equation (I) with respect to y on both sides. ∂ u ∂ y = ∂ ∂ y ( a x + b x y 2 ) = ∂ ∂ y ( a x ) + ∂ ∂ y ( b x y 2 ) = 0 − 2 b x y 3 = − 2 b x y 3 Substitute, a x + b x y 2 for u , a y + b x 2 y for v , 0 for ∂ u ∂ t , a − b x 2 y 2 for ∂ u ∂ x and − 2 b x y 3 for ∂ u ∂ y in Equation (III). a x = 0 + ( a x + b x y 2 ) ( a − b x 2 y 2 ) + ( a y + b x 2 y ) ( − 2 b x y 3 ) = ( a x + b x y 2 ) ( a − b x 2 y 2 ) + ( a y + b x 2 y ) ( − 2 b x y 3 ) = a 2 x − a b x y 2 + a b x y 2 − b 2 x 3 y 4 − 2 a b x y 2 − 2 b 2 x 3 y 4 = a 2 x − 2 a b x y 2 − 3 b 2 x 3 y 4 Thus, the acceleration along x axis is a 2 x − 2 a b x y 2 − 3 b 2 x 3 y 4 . Write the expression of y component of acceleration. a y = ∂ v ∂ t + u ∂ v ∂ x + v ∂ v ∂ y (IV) Differentiate Equation (II) with respect to t on both sides

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

Ch. 4.1 - Prob. 2P Ch. 4.1 - The velocity field of a flow is given by m/s,...Ch. 4.1 - A two-dimensional velocity field is given by u = 1...Ch. 4.1 - Streamlines are given in Cartesian coordinates by...Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P Ch. 4.1 - Prob. 11P Ch. 4.1 - Prob. 12P

Ch. 4.1 - The x and y components of a velocity field are...Ch. 4.1 - Prob. 14P Ch. 4.1 - Prob. 15P Ch. 4.1 - For any steady flow the streamlines and...Ch. 4.1 - Prob. 17P Ch. 4.1 - Prob. 18P Ch. 4.1 - Prob. 19P Ch. 4.1 - Prob. 21P Ch. 4.1 - Classify the following flows as one-, two-, or...Ch. 4.2 - Prob. 23P Ch. 4.2 - Air is delivered through a constant-diameter duct...Ch. 4.2 - Water flows through a constant diameter pipe with...Ch. 4.2 - The velocity of air in the diverging pipe shown in...Ch. 4.2 - A certain flow field has the velocity...Ch. 4.2 - Prob. 28P Ch. 4.2 - Prob. 29P Ch. 4.2 - A shock wave is a very thin layer (thickness = ℓ)...Ch. 4.2 - Estimate the average acceleration of water as it...Ch. 4.2 - Prob. 32P Ch. 4.2 - As a valve is opened, water flows through the...Ch. 4.2 - The fluid velocity along the x axis shown in Fig....Ch. 4.2 - A fluid flows along the x axis with a velocity...Ch. 4.2 - A constant-density fluid flows through a...Ch. 4.2 - Prob. 37P Ch. 4.2 - Prob. 38P Ch. 4.2 - Prob. 39P Ch. 4.2 - An incompressible fluid flows through the...Ch. 4.2 - Prob. 41P Ch. 4.2 - Prob. 42P Ch. 4.2 - Prob. 43P Ch. 4.2 - Prob. 44P Ch. 4.2 - Prob. 45P Ch. 4.2 - Prob. 46P Ch. 4.2 - Assume that the streamlines for the wingtip...Ch. 4.2 - The velocity components for steady flow through...Ch. 4.2 - Water flows through the curved hose shown in Fig....Ch. 4.2 - Water flows though the slit at the bottom of a two...Ch. 4.2 - Prob. 51P Ch. 4.2 - Prob. 52P Ch. 4.2 - Fluid flows through a pipe with a velocity of 2.0...Ch. 4.2 - A gas flows along the x axis with a speed of V =...Ch. 4.2 - Assume the temperature of the exhaust in an...Ch. 4.2 - A bicyclist leases from her home at 9 a.m. and...Ch. 4.2 - The following pressures for the air flow in...Ch. 4.4 - In the region just downstream of a sluice gate,...Ch. 4.4 - At time t = 0 the valve on an initially empty...Ch. 4.4 - From calculus, one obtains the following formula...Ch. 4.4 - Air enters an elbow with a uniform speed of 10 m/s...Ch. 4.4 - A layer of oil flows down a vertical plate as...Ch. 4.4 - Figure P4.64 shows a fixed control volume. It has...Ch. 4.4 - Water enters a 5-ft-wide, 1-ft-deep channel as...Ch. 4.4 - The wind blows across a field with an approximate...Ch. 4.4 - Water flows from a nozzle with a speed of V = 10...

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