An excellent approximation for the two-dimensionalincompressible laminar boundary layer on the flat surfacein Fig. P4.17 isfor y s8where 8 = Cx2, C = const(a) Assuming a no-slip condition at the wall, find an expressionfor the velocity component v(x, y) for ys 8. (b) Then find themaximum value of vat the station x = 1 m, for the particularcase of airflow, when U = 3 m/s and &= 1.1 cm.Layer thickness 5(x)U= constantи (х, у)u(x, y)

(a) Write the given equation for δ. δ=Cx1/2 Here, δ is the boundary layer thickness for the flow.…

Answered: An excellent approximation for the…

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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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?
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 ?
The three-arm lawn sprinkler of Fig. P3.153 receives 20 8 Cwater through the center at 2.7 m 3 /h. If collar friction isnegligible, what is the steady rotation rate in r/min for( a ) θ = 0 ° and ( b ) θ = 40 ° ?
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.
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?
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.
The small boat in Fig. P3.48 is driven at a steady speed V 0by a jet of compressed air issuing from a 3-cm-diameterhole at V e = 343 m/s. Jet exit conditions are p e = 1 atm andT e = 30 ° C. Air drag is negligible, and the hull drag is kV0 2 ,where k ≈ 19 N ? s 2 /m 2 . Estimate the boat speed V 0 in m/s.
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 uniform stream, U∞ = 4 m/s, approaches a Rankine ovalas in Fig. with a = 50 cm. Find the strength m of thesource-sink pair, in m2/s, which will cause the total lengthof the oval to be 250 cm. What is the maximum width ofthis oval?
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.
Air flows through a 6-cm-diameter smooth pipe that has a2-m-long perforated section containing 500 holes (diameter1 mm), as in Fig. . Pressure outside the pipe issea-level standard air. If p1 = 105 kPa and Q1 = 110 m3/h,estimate p2 and Q2, assuming that the holes are approximatedby thin-plate orifices. (Hint: A momentum controlvolume may be very useful.)

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