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

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Answered: Problem 6. Two immiscible fluids are…

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

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5. Two immiscible fluids of equal density are flowing down a surface inclined at a 30° angle. The two fluid layers are of equal thickness h = 2.5 mm; the kinematic viscosity of the upper fluid is twice that of the lower fluid, which is Viower-2x10 m² s. Find the velocity at the interface and the velocity at the free surface. Plot the velocity distribution.
3
A shaft (250 mm diameter) rotates at 250 rpm inside a sleeve (251 mm diameter) with a constant clearance. If the power required to rotate the shaft is 2204 W, find the viscosity of lubricant oil in the clearance. Take length of sleeve as 150 mm. Assume a linear velocity profile in the fluid film.
A cylindrical machine part moves within a surrounding cylinder. The centrelines of the part and the surrounding cylinder are coincident. The cylinder is full of an oil (viscosity 0.25kg/ms) that is not flowing i.e. no pressure gradient is applied. What is the value of the viscous force exerted on the machine part as it moves along the cylinder at a speed of 9m/s? • The machine part is 0.06m long and has a radius of 0.041m. • The ratio of the machine part radius to the cylinder radius is 0.98. • Assume that the flow is dominated by viscous forces. • Give your answer as an absolute value i.e. no negative sign, in Newtons to one decimal place.
8./A plunger is moving through a cylinder at a speed of 6 m/s, as shown in Fig. (1.8). The film of oil separating the plunger from the cylinder has a viscosity of 0.96 N. s/m?. What is the force required to maintain this motion? 0.076 m H = 0.96 N. s/m² Zeiün in. -Cylinder 6 m/s - 0.13 m ail tilm V 0.126 m Pistan Figure (1.8) Scanned with CamScanner
Laminar flow takes place between parallel plates 10 mm apart. The plates are inclined at 45° with the horizontal. For oil of viscosity 0.9 kg/m.s and mass density is 1260 kg/m³, the pressure at two points 1.0 m vertically apart are 80 kN/m2 and 250 kN/m2 when the upper plate moves at 2.00 m/s velocity relative to the lower plate but in opposite direction to flow determine velocity distribution, max. velocity and shear stress on the top plate.
An incompressible fluid (kinematic viscosity =7.4x10-7 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,find the shear stress in Pascal on the surface of top plate.
A thin film of oil of thickness Y and dynamic viscosity u flows uniformly down an inclined plane as shown in Figure Q2 (in which p is the pressure and A is the cross-sectional area of the element of fluid shown) under laminar conditions. Given that the velocity gradient is zero at the free surface and that the pressure gradient must be zero (i.e. the flow is uniform and atmospheric conditions prevail) at the surface, show that the velocity profile is pg u = (Yy- y/2) sine where u is the local velocity at an elevation y above the bed, 0 is the inclination of the plane to the horizontal and pis the fluid density. Also, du dy where t is the shear stress and du/dy is the velocity gradient. A reservoir discharges through a sluice gate that is 1.2 m wide by 1.4 m deep. The top of the opening is 0.8 m below the water level in the reservoir. The water level just downstream of the sluice gate is below the bottom of the opening. Calculate the theoretical discharge. The theoretical discharge…
Please solve following problem. Especially I cannot understand how to get flow rate.
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.
1. An oil of density p and viscosity µ, drains steadily down the side of a vertical wall, as shown. After a development region near the top of the wall, the oil film becomes independent of z and flows with a constant thickness 8. Note that the wall is very large, extending "infinitely" (compared to the thickness 8) in y and z directions. The vertical velocity can be assumed to be the only component of flow velocity. The whole flow is taking place out in the atmosphere and the atmosphere offers no shear resistance to the film. Plate Oil film Air First, reduce the continuity equation to its simplest formfor this problem by justifying each reduction/simplification. Then, using the information obtained from the continuity and other assumptions/information about the flow, reduce the remaining Navier-Stokes equations their simplest forms byjustifying each to reduction/simplification. What would you obtain if you solved the reduced equations? Do not solve the reduced equations.
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