Explanation The figure below shows the shear stresses acting on fluid element. Figure-(1) Write the expression for torque acting on left face of the element. ( T x y ) L = ( τ x y − 1 2 ∂ τ x y ∂ x d x ) ( d y × d x 2 × 1 ) (I) Here, shear stress is τ x y element length in x direction is d x and element length in y direction is d y . Write the expression for torque acting on right face of the element. ( T x y ) R = ( τ x y − 1 2 ∂ τ x y ∂ x d x ) ( d y × d x 2 × 1 ) (II) Write the expression for torque acting on bottom face of the element. ( T x y ) B = − ( τ x y − 1 2 ∂ τ x y ∂ y d x ) ( d x × d y 2 × 1 ) (III) Write the expression for torque acting on top face of the element. ( T x y ) T = − ( τ x y − 1 2 ∂ τ x y ∂ y d x ) ( d x × d y 2 × 1 ) (IV) Write the expression for total torque acting on the fluid element. T = ( T x y ) T + ( T x y ) R + ( T x y ) T + ( T x y ) B (V) Substitute − ( τ x y − 1 2 ∂ τ x y ∂ y d x ) ( d x × d y 2 × 1 ) for ( T x y ) T , − ( τ x y − 1 2 ∂ τ x y ∂ y d x ) ( d x × d y 2 × 1 ) for ( T x y ) B , ( τ x y − 1 2 ∂ τ x y ∂ x d x ) ( d y × d x 2 × 1 ) for ( T x y ) R and ( τ x y − 1 2 ∂ τ x y ∂ x d x ) ( d y × d x 2 × 1 ) for ( T x y ) L in the Equation (V). T = { − ( τ x y − 1 2 ∂ τ x y ∂ y d x ) ( d x × d y 2 × 1 ) + ( τ x y − 1 2 ∂ τ x y ∂ x d x ) ( d y × d x 2 × 1 ) + ( τ x y − 1 2 ∂ τ x y ∂ x d x ) ( d y × d x 2 × 1 ) − ( τ x y − 1 2 ∂ τ x y ∂ y d x ) ( d x × d y 2 × 1 ) } T = [ ( τ x y ) ( d x d y ) − ( τ y x ) ( d x d y ) ] T = ( τ x y − τ y x ) ( d x d y ) (VI) Write the expression for rotational equilibrium condition of the fluid element

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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Chapter 6.3, Problem 25P

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The shear stress τxy is equal to τyx.

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

Ch. 6.1 - Prob. 1P Ch. 6.1 - The velocity in a certain flow field is given by...Ch. 6.1 - The flow in the plane two-dimensional channel...Ch. 6.1 - The three components of velocity in a flow field...Ch. 6.1 - Determine an expression for the vorticity of the...Ch. 6.1 - According to Eq. 6.134, the x-velocity in fully...Ch. 6.1 - For a certain incompressible, two-dimensional flow...Ch. 6.1 - An incompressible viscous fluid is placed between...Ch. 6.1 - A viscous fluid is contained in the space between...Ch. 6.1 - ..Air is delivered through a constant-diameter...

Ch. 6.2 - For a certain incompressible flow field it is...Ch. 6.2 - Prob. 12P Ch. 6.2 - Prob. 14P Ch. 6.2 - For each of the following stream functions, with...Ch. 6.2 - The stream function for an incompressible,...Ch. 6.2 - Prob. 17P Ch. 6.2 - Prob. 18P Ch. 6.2 - In a two-dimensional, incompressible flow field,...Ch. 6.2 - The stream function for an incompressible flow...Ch. 6.2 - The stream function for an incompressible,...Ch. 6.2 - Consider the incompressible, two-dimensional flow...Ch. 6.3 - A fluid with a density of 2000 kg/m3 flows...Ch. 6.3 - Prob. 24P Ch. 6.3 - Prob. 25P Ch. 6.4 - The stream function for a given two-dimensional...Ch. 6.4 - Prob. 27P Ch. 6.4 - Prob. 28P Ch. 6.4 - Prob. 29P Ch. 6.4 - The velocity potential for a certain inviscid flow...Ch. 6.4 - Prob. 31P Ch. 6.4 - Prob. 32P Ch. 6.4 - Prob. 33P Ch. 6.4 - Prob. 34P Ch. 6.4 - Prob. 35P Ch. 6.4 - Prob. 36P Ch. 6.4 - Prob. 37P Ch. 6.5 - Prob. 38P Ch. 6.5 - Prob. 39P Ch. 6.5 - Water flows through a two-dimensional diffuser...Ch. 6.5 - Prob. 41P Ch. 6.5 - Prob. 42P Ch. 6.5 - Prob. 43P Ch. 6.5 - Prob. 44P Ch. 6.5 - Prob. 45P Ch. 6.5 - Prob. 46P Ch. 6.5 - Consider the flow of a liquid of viscosity μ and...Ch. 6.5 - Prob. 48P Ch. 6.5 - Show that the circulation of a free vortex for any...Ch. 6.5 - Prob. 50P Ch. 6.6 - Potential flow against a flat plate (Fig. P6.51a)...Ch. 6.6 - Prob. 52P Ch. 6.6 - Prob. 53P Ch. 6.6 - Prob. 54P Ch. 6.6 - Prob. 55P Ch. 6.6 - Prob. 56P Ch. 6.6 - A 15-mph wind flows over a Quonset hut having a...Ch. 6.6 - Prob. 58P Ch. 6.6 - Prob. 59P Ch. 6.6 - Prob. 60P Ch. 6.6 - Prob. 61P Ch. 6.6 - Prob. 62P Ch. 6.6 - The velocity potential for a cylinder (Fig. P6.63)...Ch. 6.6 - (See The Wide World of Fluids article titled “A...Ch. 6.6 - Prob. 65P Ch. 6.6 - Air at 25 °C flows normal to the axis of an...Ch. 6.8 - Determine the shearing stress for an...Ch. 6.8 - Prob. 68P Ch. 6.8 - The velocity of a fluid particle moving along a...Ch. 6.8 - “Stokes’s first problem” involves the...Ch. 6.9 - Oil (SAE 30) at 15.6 °C flows steadily between...Ch. 6.9 - Prob. 72P Ch. 6.9 - Prob. 73P Ch. 6.9 - We will see in Chapter 8 that the pressure drop in...Ch. 6.9 - (See The Wide World of Fluids article titled “10...Ch. 6.9 - The bearing shown in Fig. P6.76 consists of two...Ch. 6.9 - Prob. 77P Ch. 6.9 - Prob. 78P Ch. 6.9 - An incompressible, viscous fluid is placed between...Ch. 6.9 - Two immiscible, incompressible, viscous fluids...Ch. 6.9 - Prob. 81P Ch. 6.9 - A viscous fluid (specific weight = 80 lb/ft3;...Ch. 6.9 - A flat block is pulled along a horizontal flat...Ch. 6.9 - A viscosity motor/pump is shown in Fig. P6.84. The...Ch. 6.9 - A vertical shaft passes through a bearing and is...Ch. 6.9 - A viscous fluid is contained between two long...Ch. 6.9 - Verify that the momentum correction factor β for...Ch. 6.9 - Verify that the kinetic energy correction factor α...Ch. 6.9 - A simple flow system to be used for steady-flow...Ch. 6.9 - (a) Show that for Poiseuille flow in a tube of...Ch. 6.9 - An infinitely long, solid, vertical cylinder of...Ch. 6.9 - We will see in Chapter 8 that the pressure drop in...Ch. 6.9 - A liquid (viscosity = 0.002 N · s/m2; density =...Ch. 6.9 - Fluid with kinematic viscosity ν flows down an...Ch. 6.9 - Blood flows at volume rate Q in a circular tube of...Ch. 6.9 - An incompressible Newtonian fluid flows steadily...Ch. 6.9 - Prob. 97P Ch. 6.9 - Prob. 98P Ch. 6.9 - Prob. 99P Ch. 6.10 - Prob. 101P Ch. 6.10 - Prob. 102P Ch. 6.11 - Prob. 1LLP Ch. 6.11 - Prob. 2LLP Ch. 6.11 - Prob. 3LLP

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