164 Chapter 5 The Momentum Equation and its Applications5.5 A uniform pipe 75 m long containing water is fittedwith a plunger. The water is initially at rest. If the plunger isforced into the pipe in such a way that the water is acceler-ated uniformly to a velocity of 1.7 m s¹ in 1.4 s what will bethe increase of pressure on the face of the plunger assumingthat the water and the pipe are not elastic?If instead of being uniformly accelerated the plunger isdriven by a crank 0.25 m long and making 120 rev min-¹ sothat the plunger moves with simple harmonic motion, whatwould be the maximum pressure on the face of the piston?[91 kN m², 2962.5 kN m-²2]5.6 A flat plate is struck normally by a jet of water 50 mmin diameter with a velocity of 18 m s¹. Calculate (a) theforce on the plate when it is stationary, (b) the force on theplate when it moves in the same direction as the jet with avelocity of 6 m s-¹, (c) the work done per second and theefficiency in case (b).[(a) 636.2 N, (b) 282.7 N, (c) 1696.2 W, 29.6 per cent]5.7 A jet of water 50 mm in diameter with a velocity of18 m s¹ strikes a flat plate inclined at an angle of 25° to theaxis of the jet. Determine the normal force exerted on theplate (a) when the plate is stationary, (b) when the plate ismoving at 4.5 m s-¹ in the direction of the jet, and (c) deter-mine the work done and the efficiency for case (b).[(a) 269 N, (b) 151.2 N, (c) 287.55 W, 5 per cent]5.8 A jet of water delivers 85 dm³ s¹ at 36 m s¹ onto aseries of vanes moving in the same direction as the jet at18 m s¹. If stationary, the water which enters tangentiallywould be diverted through an angle of 135°. Friction re-duces the relative velocity at exit from the vanes to 0.80 ofthat at entrance. Determine the magnitude of the resultantforce on the vanes and the efficiency of the arrangement.Assume no shock at entry.[2546 N, 0.783]5.9 A 5 cm diameter jet delivering 56 litres of water persecond impinges without shock on a series of vanes movingat 12 m s¹ in the same direction as the jet. The vanes arecurved so that they would, if stationary, deflect the jetthrough an angle of 135°. Fluid resistance has the effect ofreducing the relative velocity by 10 per cent as the watertraverses the vanes. Determine (a) the magnitude and direc-tion of the resultant force on the vanes, (b) the work doneper second by the vanes and (c) the efficiency of thearrangement.[(a) 1632 N at 21°15', (b) 18.25 kW, (c) 79.7 per cent]5.10 Figure 5.25 shows a cross-section of the end of acircular duct through which air (density 1.2 kg m-³) isdischarged to atmosphere through a circumferential slot,the exit velocity being 30 m s. Find the force exerted on theduct by the air if the gauge pressure at A is 2065 N m-²below the pressure at outlet.[720.7 N]5.14 A rocket is fired vertically starting from rest. Neglectingair resistance, what velocity will it attain in 68 s if its initialmass is 13 000 kg and fuel is burnt at the rate of 124 kg s-¹,AFIGURE 5.25Water flow→0.3 mdiam5.11 Water flows throarrangement shown in Fthe horizontal plane. Thethe atmosphere as a paraand the pressure at A is 1.neglected. Find the momewater on this arrangemenpoint X.1.2 mdiamPerfectly flexiblejointFIGURE 5.261.1 mdiam8 cm diamA10 cr5.12 A ram-jet engine cand 0.6 kg of fuel per sec-is 520 m s¹ relative to th200 m s¹ absolute. What5.13 The resistance of aat a speed of um s¹. It iswith intakes facing forwabeing 0.8 and the efficiencto be driven at 3.4 m s-¹.pumped astern per seconthe pump.5.17 A lawn sprinknozzles at each end nat 40° to the horizon

Question

Accepted Answer

Hi,   As per the guidelines, we can solve only first question for you since the exact one is not…