▸ An incompressible Newtonian fluid flows between two parallel plates (distance b). The bottom plate is fixed while the upper one moves at a constant velocity V (assuming linear velocity distribution). The surfaces of the lower and upper plates are maintained at T = T₁ and T = To, respectively. Find T(y). Assume fluid viscosity and conductivity k are known. μ

▸ An incompressible Newtonian fluid flows between two parallel plates (distance b). The bottom plate is fixed while the upper one moves at a constant velocity V (assuming linear velocity distribution). The surfaces of the lower and upper plates are maintained at T = T₁ and T = To, respectively. Find T(y). Assume fluid viscosity and conductivity k are known. μ

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

Similar questions

A viscous incompressible Newtonian fluid is contained between two fixed parallel plates inclined at an angle 0, and the flow is driven by both constant pressure gradient E = constant) and gravity. The distance between the two plates is 2H and the chosen system of coordinates is shown in the figure. Assuming steady, 2D, and parallel flow (v = w = 0) and using differential analysis: (a) Show that the flow is fully developed using continuity equation; and (b) Find the velocity profile u(y) in terms of ,H,P,g,0,H de using Navier-Stokes equations with appropriate boundary conditions. 211
At a point in a pipe that lay flat ノ water in the pipe flows at a speed of 9.0 mls and has 6-40x 104 Pa a gaoge pressure is Find the gauge pressure at point 2 of pipe that lower than the first point 8.0 m and the cvoss - se ctional| area of the pipe is double of first point . Answer [1.52x105 Pa]
An incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is rt of this book may be repro
3. Consider a fluid motion at a velocity Vol with a space-time varying density such that, n(x, t) = no eα²²xVoxt Find the total time change of n(x, e) as seen by an observer co-moving with the fluid (the convective or material derivative)
(a) A Newtonian fluid having a specific gravity of 0.95 and a kinematic viscosity of 4.2 x 10“m/s flows past a fixed surface as shown in Figure la. The “no-slip" condition suggests that the velocity of the fluid at the fixed surface is zero. The fluid velocity profile away from the fixed surface is given by the equation below: и Зу 1, U 28 2 where U is the constant maximum velocity and its value is 2 m/s. Given that the shear stress developed at the fixed surface is 0.12 N/m², determine the thickness of the fluid, d. Figure la: Fluid velocity profile (b) The clutch system shown in Figure 1b is used to transmit torque through a 3 mm thick clutch oil film with µ = 0.38 Ns/m² between two identical 25 cm diameter disks. When the driving shaft rotates at a speed of 100 rpm, the driven shaft is observed to be stationary. Assuming a linear velocity profile for the oil film, determine the transmitted torque and the power required. Driving shaft Driven shaft 25 cm 3 mm Clutch oil Figure 1b:…
Q2) A block of weight W slides down an inclined plane on a thin film of oil with terminal velocity V, as shown in Figure Q2, and thus a shear stress will be existed (t). The film contact area is A and its thickness h, oil viscosity u and incline angle 0. Assuming a linear velocity distribution in the film, prove that the analytic expression for the terminal velocity can be V=(hWcos0) /Aµ. For both Group 1 and Group 2 Oil film, thickness h Figure Q2
3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. Figure for Part (a) U Figure for Part (b) 30 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p ) b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180° + 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then, calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )
Take the full-blown Couette flow as shown in the figure. While the upper plate is moving and the Lower Plate is constant, flow occurs between two infinitely parallel plates separated by the H distance. The flow is constant, uncompressed, and two-dimensional in the X-Y plane. In fluid viscosity µ, top plate velocity V, distance h, fluid density ρ, and distance y, create a dimensionless relationship for component X of fluid velocity using the method of repeating variables. Show all steps in order.
The velocity distribution in a 0.02 m diameter horizontal pipe conveying carbon tetrachloride (specific gravity = 1.59, absolute viscosity = 9.6 x 10-6 Pa sec) is given by the parabolic equation: v(r)=0.01(0.12- r?), where v(r) is the velocity in (m/s) at a distance r in (m) from the pipe center. What is discharge? O a. 3.13 x-8 m3/s O b. None of the mentioned O c. 1.047 x 108 m3/sec O d. 4.97 x 109 m3/sec
The physical model of a pipe containing water with kinematic viscosity o = 0.804 × 10-6 ™* has been built in the scale of in a laboratory. i. Find the ratio of velocity of water in the main pipe with kinematic viscosity of 8 = 2.79 x 10-4 m? to the model. ii. Discuss the difference in the velocities of the model and main pipe.
g Figure 3: Fluid flows between two infinite plates A viscous, incompressible steady fluid flows between two infinite, vertical, parallel plates distance h apart, as shown in Figure 3. Use the given coordinates system and assume that the flow is laminar, fully developed (30), and planar (w = 0,0). Assume that pressure and gravity are not negligible. (a) Simplify the contnuity equation and show that v = 0. (b) Using the y-momentum equation show that pressure is a function of a only. (c) Find the velocity distribution u(y) in terms of u, g, h, p and d (d) Find the wall shear stress of the flow.
Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow