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

8th Edition

ISBN: 9781119571490

Author: GERHART

Publisher: WILEY

See similar textbooks

Concept explainers

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. T…

Videos

Question

Chapter 6.3, Problem 25P

To determine

The shear stress τxy is equal to τyx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.3, Problem 24P

Chapter 6.4, Problem 26P

Students have asked these similar questions

36 2) Use the method of MEMBERS to determine the true magnitude and direction of the forces in members1 and 2 of the frame shown below in Fig 3.2. 300lbs/ft member-1 member-2 30° Fig 3.2. https://brightspace.cuny.edu/d21/le/content/433117/viewContent/29873977/View

Can you solve this for me?

5670 mm The apartment in the ground floor of three floors building in Fig. in Baghdad city. The details of walls, roof, windows and door are shown. The window is a double glazing and air space thickness is 1.3cm Poorly Fitted-with Storm Sash with wood strip and storm window of 0.6 cm glass thickness. The thickness of door is 2.5 cm. The door is Poor Installation. There are two peoples in each room. The height of room is 280 cm. assume the indoor design conditions are 25°C DBT and 50 RH, and moisture content of 8 gw/kga. The moisture content of outdoor is 10.5 gw/kga. Calculate heat gain for living room : الشقة في الطابق الأرضي من مبنى ثلاثة طوابق في مدينة بغداد يظهر في مخطط الشقة تفاصيل الجدران والسقف والنوافذ والباب. النافذة عبارة عن زجاج مزدوج وسمك الفراغ الهوائي 1.3 سم ضعيف الاحكام مع ساتر حماية مع إطار خشبي والنافذة بسماكة زجاج 0.6 سم سماكة الباب 2.5 سم. الباب هو تركيب ضعيف هناك شخصان في كل غرفة. ارتفاع الغرفة 280 سم. افترض أن ظروف التصميم الداخلي هي DBT25 و R50 ، ومحتوى الرطوبة 8…

Chapter 6 Solutions

FUNDAMENTALS OF FLUID MECHANICS

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The shear stress τ x y is equal to τ y x .

Concept explainers

Videos

The shear stress τxy is equal to τyx.

Want to see the full answer?

Chapter 6 Solutions