A flow develops between two parallel plates, each of area (A). The plates are separated by a gap (H) with the lower plate always fixed. The flow can be generated by imposing a constant positive pressure drop (AP/L) and/or moving the upper plate at a constant velocity UT. The general expression of the velocity in the x-direction is: only bart 3 part 1 AP u(y) = -(Hy-y²) + sgn U₁ 2μ L In the above equation μ is the fluid viscosity, and sgn=+1 if the upper plate is pulled in the positive x- direction while sgn=-1 if the upper plate is pulled in the negative x-direction. (1) Determine the expression of the drag force on the lower fixed plate in each of the following cases: Case1: Flow is driven by the moving upper plate and there is no pressure drop (AP/L =0). Case2: The flow is driven by the pressure drop but the upper plate is also fixed (UT=0) Case3: Both the pressure drop and moving upper plate are responsible for the flow. (2) Which one of the above three cases leads to the largest drag force? y H (3) Under what pressure drop would case1 and case 3 lead to the same drag force, assuming that in case 3 the upper plate is pulled back (negative x-direction) with the same velocity UT

A flow develops between two parallel plates, each of area (A). The plates are separated by a gap (H) with the lower plate always fixed. The flow can be generated by imposing a constant positive pressure drop (AP/L) and/or moving the upper plate at a constant velocity UT. The general expression of the velocity in the x-direction is: only bart 3 part 1 AP u(y) = -(Hy-y²) + sgn U₁ 2μ L In the above equation μ is the fluid viscosity, and sgn=+1 if the upper plate is pulled in the positive x- direction while sgn=-1 if the upper plate is pulled in the negative x-direction. (1) Determine the expression of the drag force on the lower fixed plate in each of the following cases: Case1: Flow is driven by the moving upper plate and there is no pressure drop (AP/L =0). Case2: The flow is driven by the pressure drop but the upper plate is also fixed (UT=0) Case3: Both the pressure drop and moving upper plate are responsible for the flow. (2) Which one of the above three cases leads to the largest drag force? y H (3) Under what pressure drop would case1 and case 3 lead to the same drag force, assuming that in case 3 the upper plate is pulled back (negative x-direction) with the same velocity UT

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

JA two-dimensional reducing bend has a linear velocity profile at section O The flow is uniform at sections and O The fluid is incompressible and the flow is steady. Find #1=0.5 the maximum velocity, V1,mav at section O V1,max 30° V3 - 5 m/s h3 - 0.15 m V2 = 1 m/s h2 - 0.2
4. Fluid flows axially in the annular space between a cylinder and a concentric rod. The radius of the rod is r; and that of the cylinder is ro. Fluid motion in the annular space is driven by an axial pressure gradient dp/dz. The cylinder is maintained at uniform temperature To. Assume incompressible laminar axisymmetric flow and neglect gravity and end effects. Show that the axial velocity is given by: _1-(r; /r, )? In(r, / r; ) r dp |(r/r,)? Au dz - In(r / r, ) – 1
The velocity components in the x and y directions are given by 3 u = Axy3 - x2y, v = xy2 -- The value of a for a possible flow field involving an incompressible fluid is
Q.4 Given below the velocity and temperature field for a flow, determine the time rate of change of temperature of the fluid particles at x = 2 m, y=2 m when t=0. V = (In x + y)î + 3xtĵ T = T,(y² + e-ax) sin(bt) with T, = 50°C a = 2 m-1 b = 1 rad/s.
A line source discharging a flow at 0.6 m/s per unit length is located at (-1,0) and a sink of volume flow rate 1.2 m2/s is located at (2,0). For a dynamic pressure of 10 N/m at the origin, determine the velocity and dynamic pressure at (1,1). Рх, у) 米 (-1, 0) (2,0)
Question 2. An incompressible fluid flows steadily in the entrance region of a two dimensional channel of height 2h. Density of the fluid is 1.24 kg/m3. The uniform velocity at the channel entrance is U1=5.3m/s The velocity distribution at a section downstream is: 1- ()* и Umax Find out the maximum velocity umax in the downstream section in (m/s).
Thevelocity components in thex and y directions are given by u = Ary3 – x²y, v = xy? -÷y*. The value of 1 for a possible flow field involving an incompressible fluid is
The entrance flow between two parallel plates (gap h) has a velocity that varies linearly at the entrance and develops into a fully parabolic profile at the exit. What is the relationship between the maximum velocity at the entrance and that at the exit? You can show by symmetry that the maximum velocity is attained at the mid-plane between the two plates.
a) The velocity in a certain flow field is given by the equation below, V = (x² - y²)ī — 2xyj Show that the flow is irrotational and satisfies the conservation of mass.
The reduced elbow shown in the figure is part of a distribution system for a fluid whose density is 0.85 and which is in a vertical plane. If the manometer at point 1 indicates 245 kPa, and the flow rate at point 1 is 0.060 m/s. a) Calculate the reactions at "x" and "y" at A to keep the elbow in place
I) A fluid flow field is givenby:? = − 3 ?4?? + ?3?? − (5 ??? − ??7) ?. Calculate the acceleration at the point (2,5,3). ii) A pipe of diameter 400 mm carries water at a velocity of 25 m/s. The pressure at the point A and B are given as 29.43 N/cm2 and 22.563 N/cm2 respectively while the datum head at A and B are 28 m and 30 m. Find the loss of head between A andB. III) A horizontal pipe line 40 m long is connected to a water tank at one end and discharges freely into the atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is 150 mm diameter and its diameter are suddenly enlarged to 300 mm. The height of water level in the tankis8mabovethecentreofthepipe.Consideringalllossesofheadwhichoccur,determinethe rate of flow. Take f = 0.01 for both sections of thepipe. Iv) Two pipes of identical length and material are connected in parallel. The diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to be the same in both cases and…
5. A linear velocity profile is formed in a fluid between two plates as shown in the figure when one of the plates is moved parallel to the other and there is no externally imposed pressure gradient (i.e. there is no pump). If the top plate is travels at U = 0.3 m/s and the bottom plate is held fixed and the two plates are separated by a distance d = 0.3 m/s, derive an equation for the velocity profile u(y). Assume that the fluid in contact with either plate moves at the same speed as the plate (this is called the no-slip condition). U=0.3 m/s d=0.3 m