3. Consider a viscous flow between two flat plates separated by a distance H. The bottom plate islocated at y = 0 and moves to the right with speed Uplate. The top plate is located at y = H andmoves to the left with speed 2Uplate. The pressure in the flow is constant. The fluid between theplates has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, twodimensional, and has negligible body forces. Starting from the differential form of the conservationof mass and momentum equations:a. Derive an equation for the velocity between the plates in terms of Uplate, H, and y.b. Determine the average velocity between the plates in terms of Uplate and H.C. Determine the shear stress acting on the bottom plate in terms of Uplate, H, and µ.2UplateyfluidHUplate

The flow velocity is variable between the plate. The cause behind the variable velocity is due to…

3. Consider a viscous flow between two flat plates separated by a distance H. The bottom located at y = 0 and moves to the right with speed Uplate. The top plate is located at y moves to the left with speed 2Uplate. The pressure in the flow is constant. The fluid be plates has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-de dimensional, and has negligible body forces. Starting from the differential form of the c of mass and momentum equations: a. Derive an equation for the velocity between the plates in terms of Uplate, H, ar b. Determine the average velocity between the plates in terms of Uplate and H. Determine the shear stress acting on the bottom plate in terms of Uplate, H, ar C. 2Uplate fluid H

3. Consider a viscous flow between two flat plates separated by a distance H. The bottom located at y = 0 and moves to the right with speed Uplate. The top plate is located at y moves to the left with speed 2Uplate. The pressure in the flow is constant. The fluid be plates has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-de dimensional, and has negligible body forces. Starting from the differential form of the c of mass and momentum equations: a. Derive an equation for the velocity between the plates in terms of Uplate, H, ar b. Determine the average velocity between the plates in terms of Uplate and H. Determine the shear stress acting on the bottom plate in terms of Uplate, H, ar C. 2Uplate fluid H

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and…

A: The type of deformation experienced.Given:The velocity field is .

Q: 3.7. In Fig. 3.4b is shown the unsteady-state streamlines of a cylinder moving with a uniform…

A: Dear Student,In this question, the figure (diagram) is missing. Please reupload the question with…

Q: A non-viscous fluid is flowing through the pipe as shown. At which location is the pressure the…

Q: Q3) The velocity field for a two dimensional steady and incompressible fluid flow given as: V =(-3x°…

Q: Please don't provide handwritten solution.

A: a. The maximum velocity at section 2 is given by:u(y)=hU0ySo at y=h (i.e., at section…

Q: Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and…

A: Two-dimensional flowVelocity fields,u = 1 andv = 2yt

Q: The stream function for a two-dimensional flow is Y = (0.5x² -y²) m²/s where x and y are in meters.…

Q: Under which of the following conditions can the viscous forces be neglected? O when all velocity…

A: Introduction The viscous force is the fluid's internal resistance force in response to the…

Q: An incompressible frictionless flow field is given by V = (Ax + By)i + (Bx – Ay)j where A = 1 si and…

A: The term "velocity field" refers to the dispersion of velocity in a flow zone. It is written as…

Q: 3. Consider a fluid motion at a velocity = Voi with a space-time varying density such that, n(x, t)…

Q: Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and…

A: Given that :Flow is two dimensional flowVelocity field terms are given u=1v=2ytAsking to calculate…

Q: A potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy .…

A: From given information:

Q: in Figure Q1(b). The two plates move in opposite directions with constant velocities V, and V2.…

Q: Problem 3: Obtaining the stream function from velocity components The steady state, incompressible…

Q: velocity field is given by: A two-dimensional V = (x - 2y) ï- (2x + y) j a. Show that the flow is…

A: V= (x-2y) i^- (2x+y) j^

Q: or the velocity field: u = 3xy, v = -1.5y²+5; for water, ρ = 1000 kg/m³ If the pressure at (0,0) is…

A: The velocity field is .The density of water is .The pressure at is .

Q: Two infinite plates a distance h apart are parallel to the xzplane with the upper plate moving at…

A: Since the shear stress between the parallel plates is constant, the centreline velocity will be…

Q: Consider the following steady, two-dimensional, incompressible velocity field: V = (u, v) = (ax +…

A: solution: V=(u,v)=(ax+by2)i+(bx2-ay)ju =ax+by2v =…

Question

3. Consider a viscous flow between two flat plates separated by a distance H. The bottom plate is
located at y = 0 and moves to the right with speed Uplate. The top plate is located at y = H and
moves to the left with speed 2Uplate. The pressure in the flow is constant. The fluid between the
plates has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, two
dimensional, and has negligible body forces. Starting from the differential form of the conservation
of mass and momentum equations:
a. Derive an equation for the velocity between the plates in terms of Uplate, H, and y.
b. Determine the average velocity between the plates in terms of Uplate and H.
C. Determine the shear stress acting on the bottom plate in terms of Uplate, H, and µ.
2Uplate
y
fluid
H
Uplate

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Define the flow and assumpations.

VIEW

Step 2: Apply the navier stokes equation.

VIEW

Step 3: (a)- Obtain the velocities and shear stress as follows.

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 12 images

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

A2 A Newtonian fluid with viscosity (Mu) flows upward at a steady rate between two parallel plates that make an angle y with the horizontal. The fluid thickness h is much smaller than the width of the channel W. The pressures at each end, P(0) and P(L), are known and the pressure variations in the y-direction are small. Assume that Vy and Vz = 0 and Vx is a function of y alone. Use the shell balance to approach : - the Total flowrate, QV
Please solve the following fluid mechanics questions
A Newtonian fluid is flowing in the narrow gap between two infinite parallel horizontal plates due to the movement of the top plate (see the figure below). The top plate is moving at a speed U from left to right, and the bottom plate is stationary. Consider the flow is steady, incompressible, and laminar. The distance between two plate is H, and the gravity acts in negative z-direction (which is perpendicular into the page). There is an applied constant pressure gradient of apJəx in the x-direction. Calculate the velocity and pressure fields. Plot typical velocity profiles in dimensionless form for a pressure gradient value of 0 and -15. In your solution show the conceptual diagram of the problem; write all relevant assumptions and boundary conditions; show the detailed steps of the problem solutions including equations and detailed processing of those equations. Moving plate Fluid: p.H Fixed plate P2-P1
4. Consider a viscous flow inside an annular pipe. The inner surface of the pipe is located at r = R₁ and is stationary. The outer surface is located at r = Ro and moves to the right with speed Upipe. The pressure inside the pipe is constant. The fluid inside the pipe has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, axisymmetric, non-rotating, and has negligible body forces. Starting from the differential form of the conservation of mass and momentum equations: a. Derive an equation for the velocity inside the pipe in terms of Upipe, R₁, Ro, and r. b. Determine the average velocity inside the pipe in terms of Upipe, R₁, and Ro. C. Determine the shear stress acting on the inner annulus in terms of Upipe, Ri, Ro, and u. Upipe er R₁ fluid
Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Do the fluid elements experience angular rotation? Thus, state whether the flow field is rotational or irrotational.
Problem 3: Obtaining the stream function from velocity components The steady state, incompressible flow field for two-dimensional flow is given by the following velocity components: V =16y-x and v, =16x + y %3D Determine the equation for the stream function and make sure continuity is satisfied.