The flow pattern in bearing lubrication can be illustrated byFig. P4.83, where a viscous oil (p, µ) is forced into the gaph(x) between a fixed slipper block and a wall moving atvelocity U. If the gap is thin, h< L, it can be shown that thepressure and velocity distributions are of the form p = p(x),u = u(y), v = w = 0. Neglecting gravity, reduce theNavier-Stokes rquations .. to a single differentialequation for u(y). What are the proper boundary conditions?Integrate and show that1 dp ( – yh) + U(и2д dxwhere h = h(x) may be an arbitrary, slowly varying gapwidth. (OilinletFixed slipperblockOiloutlethoh(x)и (у)Moving wall

The boundary conditions for the given pattern of the bearing lubrication can be determined from its…

Answered: The flow pattern in bearing lubrication…

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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For the pitot-static pressure arrangement of Fig.,the manometer fluid is (colored) water at 20°C. Estimate(a) the centerline velocity, (b) the pipe volume flow, and(c) the (smooth) wall shear stress.
Water at 20 ° C flows down through a vertical, 6-cm diametertube at 300 gal/min, as in Fig. P3.74. The flowthen turns horizontally and exits through a 90 ° radial ductsegment 1 cm thick, as shown. If the radial outflow is uniformand steady, estimate the forces ( F x , F y , F z ) required tosupport this system against fluid momentum changes.
As can often be seen in a kitchen sink when the faucet isrunning, a high-speed channel fl ow ( V 1 , h 1 ) may “jump” toa low-speed, low-energy condition ( V 2 , h 2 ) as in Fig. . The pressure at sections 1 and 2 is approximately hydrostatic,and wall friction is negligible. Use the continuity andmomentum relations to fi nd h 2 and V 2 in terms of ( h 1 , V 1 ).
Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Consider a venturi with a small hole drilled in the side of the throat. Thishole is connected via a tube to a closed reservoir. The purpose of theventuri is to create a vacuum in the reservoir when the venturi is placed inan airstream. (The vacuum is defined as the pressure difference below theoutside ambient pressure.) The venturi has a throat-to-inlet area ratio of0.85. Calculate the maximum vacuum obtainable in the reservoir when theventuri is placed in an airstream of 90 m/s at standard sea level conditions.
A belt moves upward at velocity V, dragging a fi lm ofviscous liquid of thickness h , as in Fig. . Near the belt,the fi lm moves upward due to no slip. At its outer edge, thefi lm moves downward due to gravity. Assuming thatthe only nonzero velocity is υ ( x ), with zero shear stress atthe outer fi lm edge, derive a formula for ( a ) υ ( x ), ( b ) the average velocity V avg in the fi lm, and ( c ) the velocity V c forwhich there is no net flow either up or down. ( d ) Sketchυ ( x ) for case ( c ).
Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Consider the nonlifting flow over a circular cylinder of a given radius,where V∞ = 20 ft/s. If V∞ is doubled, that is, V∞ = 40 ft/s, does theshape of the streamlines change? Explain.
In Prob. it would be difficult to solve for Ω because of itappears in all three of the dimensionless pump coefficients.Suppose that, in Prob. 5.61, Ω is unknown but D = 12 cmand Q = 25 m 3 /h. The fluid is gasoline at 20 ° C. Rescale thecoefficients, , to make a plot ofdimensionless power versus dimensionless rotation speed.Enter this plot to find the maximum rotation speed Ωforwhich the power will not exceed 300 W.
An engineer claims that the flow of SAE 30W oil, at 20 °C,through a 5-cm-diameter smooth pipe at 1 million N/h, islaminar. Do you agree? A million newtons is a lot, so thissounds like an awfully high flow rate.
The boat in Fig. P3.88 is jet-propelled by a pump thatdevelops a volume flow rate Q and ejects water out thestern at velocity V j . If the boat drag force is F = kV 2 , wherek is a constant, develop a formula for the steady forwardspeed V of the boat.
Q2: The pipe flow in Fig. 2 is driven by pressurized air in the tank. What gage pressure pl is needed to provide water flow rate Q=75 m/h?. Take: roughness 0.002 m, viscosity = 0.001 Kems and density - 998 kg/m³
tall water tank discharges through a well-rounded orifi ce,as in Fig. P3.95. Use the Torricelli formula to estimate the exit velocity. ( a ) If, at this instant, the forceF required to hold the plate is 40 N, what is the depth h ?( b ) If the tank surface is dropping at the rate of 2.5 cm/s,what is the tank diameter D ?
Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2(2116 lb/ft2), respectively. Prove that the flow field specified is not incompressible;i.e., it is a compressible flow as stated without proof .

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