To determine The acceleration of the fluid particle at ( x = 0.3 and t = 1 s ) Explanation Given: The velocity of the particle at point A is V A = 5 t 1 / 2 m/s . Particle location ( x ) is 0.3 m at t = 1 s . Calculation: Draw the fixed control volume as in Figure (1). Draw the cross sectional view of system as shown in figure (2). Since the volume does not change over time, no local changes occur within this control volume. From figure (1). Calculate the radius of pipe r . r − 0.05 m 0.05 m = 0.4 m − x 0.4 r = ( 0.1 − 0.125 x ) m Here, x is arbitrary distance. Calculate the velocity of the particle ( V ) . ∂ ∂ t ∫ c v ρ d V + ∂ ∂ t ∫ c s ρ V ⋅ d A = 0 0 − V A A A + V A = 0 − V A × π 4 × D A 2 + V × π r 2 = 0 − ( 5 t 1 / 2 ) × π 4 × ( 0.2 m ) 2 + V × π ( 0.1 m − 0.125 x m ) 2 = 0 V = 0.05 t 1 / 2 ( 0.1 − 0.125 x ) 2 m/s Here, average velocity of the linseed oil is V A and diameter of the pipe is D . Calculate the acceleration of the fluid particle a . a = ∂ V ∂ t + V ∂ V ∂ x a = ∂ ∂ t [ 0.05 t 1 / 2 ( 0

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Author: Russell C. Hibbeler

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The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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Chapter 4, Problem 51P

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The acceleration of the fluid particle at (x=0.3 and t=1 s)

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Chapter 4, Problem 50P

Chapter 4, Problem 52P

Chapter 4 Solutions

Fluid Mechanics (2nd Edition)

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