P4.88 The viscous oil in Fig. P4.88 is set into steady motion by a concentric inner cylinder moving axially at velocity U inside a fixed outer cylinder. Assuming constant pressure and density and a purely axial fluid motion, solve Eqs. (4.38) for the fluid velocity distribution vz(r). What are the proper boundary conditions? b v,(r) a Oil: p. µ

P4.88 The viscous oil in Fig. P4.88 is set into steady motion by a concentric inner cylinder moving axially at velocity U inside a fixed outer cylinder. Assuming constant pressure and density and a purely axial fluid motion, solve Eqs. (4.38) for the fluid velocity distribution vz(r). What are the proper boundary conditions? b v,(r) a Oil: p. µ

Name: P4.88 The viscous oil in Fig. P4.88 is set intosteady motion by a con
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Description: P4.88 The viscous oil in Fig. P4.88 is set intosteady motion by a concentric inner cylindermoving axially at velocity U inside a fixedouter cylinder. Assuming constant pressure anddensity and a purely axial fluid motion, solveEqs. (4.38) for the flu

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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The viscous oil in Fig. P4.88 is set into steady motion by aconcentric inner cylinder moving axially at velocity Uinside a fixed outer cylinder. Assuming constant pressureand density and purely axial fluid motion, solve Eqs. for the fluid velocity distribution υ z ( r ). What are theproper boundary conditions?
Incompressible steady fl ow in the inlet between parallelplates in Fig. P3.17 is uniform, u = U 0 = 8 cm/s, whiledownstream the fl ow develops into the parabolic laminar profile u = az ( z 0 - z ), where a is a constant. If z 0 = 4 cm and thefl uid is SAE 30 oil at 20 ° C, what is the value of u max in cm/s?
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 ).
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.
In elementary compressible fl ow theory , compressedair will exhaust from a small hole in a tank at themass fl ow rate m # ≈ C ρ , where ρ is the air density in thetank and C is a constant. If ρ 0 is the initial density in a tankof volume 9 , derive a formula for the density change ρ ( t )after the hole is opened. Apply your formula to the followingcase: a spherical tank of diameter 50 cm, with initialpressure 300 kPa and temperature 100 ° C, and a hole whoseinitial exhaust rate is 0.01 kg/s. Find the time required forthe tank density to drop by 50 percent.
A liquid jet of velocity V j and diameter D j strikes a fi xedhollow cone, as in Fig. P3.47, and defl ects back as a conicalsheet at the same velocity. Find the cone angle θ for whichthe restraining force F = 3/2ρAjVj2 .
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 ?
For the container of Fig. P3.116 use Bernoulli’s equation toderive a formula for the distance X where the free jet leavinghorizontally will strike the fl oor, as a function of h andH . For what ratio h / H will X be maximum? Sketch the threetrajectories for h / H = 0.25, 0.5, and 0.75.
Consider a steady, two-dimensional, incompressible fl owof a newtonian fl uid in which the velocity fi eld isknown: u = - 2 xy , υ = y 2 - x 2 , w = 0. ( a ) Does thisfl ow satisfy conservation of mass? ( b ) Find the pressurefi eld, p ( x , y ) if the pressure at the point ( x = 0, y = 0) isequal to p a .
A 7-cm-diameter solid aluminum ball (SG = 2.7) and asolid brass ball (SG = 8.5) balance nicely when submergedin a liquid, as in Fig. ( a ) If the fluid is water at20 ° C, what is the diameter of the brass ball? ( b ) If thebrass ball has a diameter of 3.8 cm, what is the density ofthe fluid?
A two-dimensional, incompressible, frictionless fluid isguided by wedge-shaped walls into a small slot at theorigin, as in Fig. P4.52. The width into the paper is b , and the volume flow rate is Q . At any given distance r fromthe slot, the flow is radial inward, with constant velocity.Find an expression for the polar coordinate stream functionof this flow.
A 3-in diameter horizontal water jet having a velocity of 140 ft/s strikes a curved plate, which deflects the water 180 degrees at the same speed. Ignoring the frictional effects, determine the force required to hold the plate against the water stream. Please no conversion need it, only the 3in into .25feet, please. for me, I got 3.71KN on the x-axis.