A10_Fluid_Mechanics_ans

A10_Fluid_Mechanics_ans - 2 of 2 V h 1 2 d 3. The Pitot...

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ASSIGNMENT 9 EATS 2470 1 of 2 EATS 2470 Introduction to Continuum Mechanics Assignment #10 - Solutions ASSIGNMENT 10 1. A solid sphere of radius R and average mass density ρ s is completely submerges in a tank filled with water of mass density w with s < w . It is held in place by a string attached to the bottom of the tank, as shown. Taking the acceleration of gravity as g . Find the tension T of the string. R T g s w Solution: T + V s s g = V s w g V s = 3 4 3 R π – the volume of sphere T = V s g ( w - s ) = 3 4 3 R g ( w - s ) 2. Verify the Navier-Stokes equations for a compressible fluid with zero bulk viscosity can be written as jj i ij j i i i q q p f q , , ~ ~ 3 1 , 1 μ + + - = Solution: The zero bulk viscosity implies λ κ ~ ~ ~ 3 2 + = =0 b ~ ~ 3 2 - = Substitute above relation into Navier-Stokes Equation, ( ) jj , i ij , j i i i q ~ q ~ ~ , p f q + + + - = 1 We have jj i ij j i i i q q p f q , , ~ ~ 3 1 , 1 + + - = &
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ASSIGNMENT 9 EATS 2470
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Unformatted text preview: 2 of 2 V h 1 2 d 3. The Pitot tube measures the fluid flow velocity by converting the kinetic energy of the flow into potential energy, as shown in the figure. V h Derive the relationship between the fluid flow velocity ( V ) and the fluid height ( h ) in the Pitot tube using Burnoulli Equation. Solution: The Burnoulli equation is 2 2 2 2 1 2 1 1 2 2 gy v p gy v p + + = + + Consider the pressure and fluid velocity at point 1 and 2 as shown in the right figure, @ Point 1 gd p p a + = 1 V v = 1 1 = y @ Point 2 a p p = 2 2 = v h d y + = 2 Then, ( ) h d g p V gd p a a + + = + + 2 2 gh V 2 2 =...
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A10_Fluid_Mechanics_ans - 2 of 2 V h 1 2 d 3. The Pitot...

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