P7.11 Air at 20°C and 1 atm flows at 2 m/s past a sharp flat plate. Assuming that the Kármán parabolic-profile analysis, Eqs. (7.6-7.10), is accurate, estimate (a) the local velocity u; and (b) the local shear stress 7 at the position (x, y) = (50 cm, 5 mm).

The bottom of a river has a 4-m-high bump that approximates a Rankine half-body, as in Fig.  The pressure at point B on the bottom is 130 kPa, and the river velocity is 2.5 m/s. Use inviscid theory to estimate the water pressure at point A on the bump, which is 2 m above point B.

A buoyant ball of specific gravity SG < 1 dropped intowater at inlet velocity V0 will penetrate a distance h andthen pop out again, as in Fig.  Make a dynamicanalysis of this problem, assuming a constant drag coefficient,and derive an expression for h as a function ofthe system properties. How far will a 5-cm-diameterball with SG = 0.5 and CD ≈ 0.47 penetrate if it entersat 10 m/s?

A rotating dishwasher arm delivers at 60 ° C to six nozzles,as in Fig.. The total fl ow rate is 3.0 gal/min. Eachnozzle has a diameter of 3/16 in. If the nozzle fl ows are equaland friction is neglected, estimate the steady rotation rateof the arm, in r/min.

Water at 20°C flows past a 1-m-diameter circular cylinder.The upstream centerline pressure is 128,500 Pa. If the lowestpressure on the cylinder surface is exactly the vaporpressure, estimate, by potential theory, the stream velocity.

Air at 20°C and 1 atm enters a 40-cm-square duct as in Fig.P7.7. Using the “displacement thickness” concept estimate (a) the mean velocity and (b) the mean pressure inthe core of the flow at the position x = 3 m. (c) What is theaverage gradient, in Pa/m, in this section?

A number of straight 25-cm-long microtubes of diameter dare bundled together into a “honeycomb” whose totalcross-sectional area is 0.0006 m 2 . The pressure drop fromthe entrance to exit is 1.5 kPa. It is desired that the total volumeflow rate be 5 m 3 /h of water at 20 ° C. ( a ) What is theappropriate microtube diameter? ( b ) How many microtubesare in the bundle? ( c ) What is the Reynolds numberof each microtube?

Consider the smooth square 10-cm-by-10-cm duct inFig. P7.25. The fluid is air at 20°C and 1 atm, flowing atVavg = 24 m/s. It is desired to increase the pressure dropover the 1-m length by adding sharp 8-mm-long flatplates across the duct, as shown. (a) Estimate the pressuredrop if there are no plates. (b) Estimate how manyplates are needed to generate an additional 100 Pa ofpressure drop.

fluidmechanics

A Rankine oval 2 m long and 1 m high is immersed in astream U∞ = 10 m/s, as in Fig. . Estimate (a) thevelocity at point A and (b) the location of point B where aparticle approaching the stagnation point achieves its maximumdeceleration.