An incompressible fluid flows between two infinite stationary parallel plates. The velocity profile is given by u =umax (Ay² + By + C), where A, B, and C are constants and y is measured upward from the lower plate. The total gap width is h. Use appropriate boundary conditions to express the constants in terms of h. Develop an expression for volume flow rate per unit depth and evaluate the ratio V/u max.

An incompressible fluid flows between two infinite stationary parallel plates. The velocity profile is given by u =umax (Ay² + By + C), where A, B, and C are constants and y is measured upward from the lower plate. The total gap width is h. Use appropriate boundary conditions to express the constants in terms of h. Develop an expression for volume flow rate per unit depth and evaluate the ratio V/u max.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.3P: Evaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK,...

See similar textbooks

Similar questions

The expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.
A venturi tube is used to determine the airspeed at the throat/test section. During the test, a raise of 4.8 inches of water was recorded in the instrument. Determine the velocity of the at the (a) smallest and (b) largest section, when the ratio of the area between the largest and smallest section is 75:30. Assume incompressible flow and standard sea-level conditions.the answer should be v1 = 63.1962 ft/s and v2 = 157.9905 ft/s
1. The components of velocity in a flow field are given byu=x2+y2+z2v=xy+yz+z2w=-3xz- 0.5z2+4a) Determine the volumetric dilatation rate and interpret the result.b) Determine an expression for the rotation vector. Is this an irrotational flow field?
A horizontal nozzle discharges water into the atmosphere as shown in the figure. the relative pressure at point 1 equal to ?1 = 18 ??? . A. A Pitot tube connected to a mercury manometer is inserted into the flow. in the area section A1 indicating a height difference ℎ = 0.01 m. For this reading indicated in the Pitot tube, determine the velocity in the A1 area section of the nozzle. B. For the dimensioning of the anchor block it is necessary to determine the force that the nozzle applies over the fluid. Calculate the component of this force in the x direction. Data: ?1 = 0.070 ?; ?2 = 0.060 ?; ? = 30°; ??? = 13.6
The velocity for the 2-dimensional flow is defined by V =(3y2 i+4xj) m/s, where y is in meters. Determine the equation of the streamline that passes through point (2 m, 1 m). only HANDWRITTEN answer needed ( NOT TYPED)
Air flows along a horizontal, curved streamline with a 5.486 m radius with a speed of 31.09 m/s. Determine the magnitude of pressure gradient normal to the streamline. Take rho = 1.2266 kg/m3
When a viscous, incompressible fluid enters a pipe of radius, R, its velocity is uniform and of magnitude U0. The fluid eventually becomes fully-developed, at which point it has a parabolic velocity profile described by the equation u(r) = Umax[ 1 − ( r/R )^2 ] , where r is the radial distance measured from the center line of the pipe. Determine an expression for the ratio of the max velocity of the fully-developed pipe flow to the uniform inlet velocity, Umax/U0. The fluid is flowing steadily
The block of weight W = 50 N is pulled by a weight W0 = 60 N along the surface of a table by means of an inextensible cable and a pulley. Between the block and the table there is a uniform layer of oil of viscosity m = 0.1 Pa-s and clearance h = 2 mm. The contact area is 0.01 m2. Find the terminal velocity U if the table is very long.
2- Consider the flow in rectangular coordinates given by v=i(X3Y)+j(2yx2z). Based on the continuity equation, verify that the fluid is compressible.
Consider a 2-dimensional incompressible flow field. The vertical component of velocity forthe flow field is given by 2y. The pressure at (x, y) = 0,0 is given by 3 bar absolute. The densityof the fluid is 1.2 Kg/m3 . Find. a) x-component of velocity; b) acceleration at point (x, y) = 2,1;c) pressure gradient at the same point; d) pressure gradient along the x-axis; e) check whetherthe flow is irrotational; f) find the potential function; g) find the stream function; h) equationfor streamline and sketch few streamlines.
The velocity field for an incompressible flow is given by V = 5x ^ 2i- 20 xyj + 100tk. Explain whether this flow is steady or not. Is the flow two or three dimensional? Determine the magnitude and direction of the velocity and acceleration of a flow particle at t = 0.2 and position (1, 2, 3).
If the stream function is y = 2xy, then the velocity at a point (1, 2) is equal to: