Problem 6. Two immiscible fluids are contained between two infinite parallel plates. The plates are separated by distance 2h, and the two fluid layers are of equal thickness h. The dynamic viscosity of the upper layer (fluid B) is three times that of the lower layer (fluid A). Find the velocity at the interface if the lower plate is stationary and the upper plate moves at constant speed, U = 20 ft/s. Assume laminar flows, and that the pressure gradient in the direction of flow is zero.

Problem 6. Two immiscible fluids are contained between two infinite parallel plates. The plates are separated by distance 2h, and the two fluid layers are of equal thickness h. The dynamic viscosity of the upper layer (fluid B) is three times that of the lower layer (fluid A). Find the velocity at the interface if the lower plate is stationary and the upper plate moves at constant speed, U = 20 ft/s. Assume laminar flows, and that the pressure gradient in the direction of flow is zero.

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

The rotating parts of a hydroelectric power plant having power capacity W . have a rotational synchronous speed n .. The weight of the rotating parts (the hydroturbine and its electric generator) is supported in a thrust bearing having annular form between D and d diameters as sketched. The thrust bearing is operated with a very thin oil film of thickness e and dynamic viscosity ? . It is assumed that the oil is a Newtonian fluid and the velocity is approximated as linear in the bearing. Calculate the ratio of lost power in the thrust bearing to the produced power in the hydraulic power plant. Use W . = 48.6 MW, ? = 0.035 Pa⋅s, n . = 500 rpm, e = 0.25 mm, D = 3.2 m, and d = 2.4 m.
Question 1. The apparatus shown in the figure is used to coat a thin steel plate with oil. Fluid1 is oil with a viscosity of 0.02 Pa.s, Fluid2 is 0.001 Pa.s. If h = 4 mm and the total oil-steel contact area is 20 m², calculate the force required to move the steel at 5 m/s. Suppose the velocity profile in the fluid is linear.
Problem 1 – A laminar flow fluid of known density (ρ) and viscosity (μ) flows between twoparallel plates with different velocities in the same direction. The top plate has a velocity Utop inthe positive x direction. The bottom plate has a velocity Ubot in the positive x direction. The twoplates are a distance of “a” apart. There is a pressure gradient in the x direction ( ). Derivean expression of the velocity and shear stress profiles between the two plates
At 60°C the surface tension of mercury is 0.47 N/m. What capillary height changes (mm) will occur in this fluid when it is in contact with air in a glass tube of radius 0.25 mm? Use wetting angle = 130° and unit weight = 132,300 N/m3
Two parallel flat plates are spaced 2 in. apart. One plate is moving at a velocity of 10 ft/min and the other is moving in the opposite direction at 35 ft/min. The viscosity of the fluid between the plates is constant at 363 lb/ft-hr. Calculate the stress on each plate. Calculate the fluid velocity profile expression for the system and fluid velocities at ½ in. intervals from plate to plate.
A square plate of size 1 m x 1m and weighing 350 N slides down an inclined plane with a uniform velocity of 1.5 m/s. The inclined plane is laid on a slope of 5 vertical to 12 horizontal and has an oil film of 1 mm thickness. Calculate the dynamic viscosity of oil in poise.
A square plate of size 1 m x 1m and weighing 350 N slides down an inclined plane with a uniform velocity of 1.5 m/s. The inclined plane is laid on a sloipe of 5 vertical to 12 horizontal and has an oil film of 1 mm thickness. Calculate the dynamic viscosity of oil in poise.
solve a and b. A shaft 80 mm in diameter is being pushed through a bearing sleeve 80.2mm in diameter and 0.3 m long. The clearance, assumed uniform is flooded with lubricating oil of viscosity 0.1 kg/ms. (a) If the shaft moves axially at 0.8 m/s, estimate the resistance force exerted by the oil on the shaft, (b) If the shaft is axially fixed and rotated at 1800 rpm, estimate the resisting torque exerted by the oil and the power required to rotate the shaft.
A large plate is pulled at a constant speed of U = 4 m/s over a fixed plate on 5-mm-thick engine oil film at 20°C. Assuming a half-parabolic velocity profile in the oil film, as sketched, determine the shear stress developed on the upper plate and its direction. What would happen if a linear velocity profile were assumed?
Consider the geometry sketched. The velocity of the upper plate is 200 ft/s, and the two plates are separated by a distance of 0.01 in. The fluid between the plates is air. Assume incompressible flow. The temperature of both plates is the standard sea level value of 519◦R.(a) Calculate the velocity in the middle of the flow.(b) Calculate the shear stress.(c) Calculate the maximum temperature in the flow.(d) Calculate the heat transfer to either wall.(e) If the lower wall is suddenly made adiabatic, calculate its temperature.
Methane gas is being pumped through a 305-m length of 52.5-mm-ID steel pipe at the rate of 41.0 kg/m2• s. The inlet pressure is P1 = 345 kPa abs. Assume isothermal flow at 288.8 K.a. Calculate the pressure P2 at the end of the pipe. The viscosity is 1.04 x 10 5 Pa·s.b. Calculate the maximum velocity that can be attained at these conditions and compare with the velocity in part (a).
You have a container like the one shown in figure 1 from which you want to extract liquid with the help of asiphon (inverted U-shaped tube). The siphon should be filled initially, but once this is done theliquid will flow until its level drops below opening A. The liquid has a density ?, and anegligible viscosity. Assume that the area of the container is very large compared to the area of thetube and that both the tube at C and the container itself at D are open to the atmosphere. a) Using Bernoulli's equation and comparing points "D" and "C", determine the speed with which the liquid flows in C. b) What is the gauge pressure of the liquid at the highest point (B)? c) What maximum height H can the highest point (B) of the tube have without ceasing to have flow? d) If the liquid of density ? is changed, for one with density ?2 where ? < ?2, will there be any change in velocity at C? If there is any change, write down with which liquid the highest speed is obtained in C, otherwise…