Chapter 12d Homework Bernoulli's Principle Qu. 1 At one point in a ...

Chapter 12d HomeworkBernoulli’s PrincipleQu. 1 At one point in a pipeline the water has a speed of 3 m/s and the gaugepressure is 5 x 10 4 Pa. Find the gauge pressure at a second point in the line,11 m lower than the first, if the pipe diameter at the second point is twicethat at the first.(Ans: 1.62 x 10 5 Pa)Qu. 2 Air streams horizontally past a small airplane’s wings such that thespeed is 70 m/s over the top surface and 60 m/s past the bottom surface. Ifthe plane has a mass 1340 kg and a wing area 16.2 m 2 , what is the netvertical force (including the effects of gravity) on the airplane ? The densityof air is 1.2 kg/m3.(Ans: 496 N down)Qu. 3 In 1993 the radius of Hurricane Emily was about 350 km. The windspeed near the center (“eye”) of the hurricane, whose radius was about 30km, reached 200 km/h. As air swirled in from the rim of the hurricanetoward the eye, it’s angular momentum remained roughly constant.a) Estimate the wind speed at the rim of the hurricane. (Ans: 4.76 m/s)b) Estimate the pressure difference at the earth’s surface between the eyeand the rim. (Ans: - 1.83 x 10 3 Pa)c) Where is the pressure greater? (Ans: Pressure is higher in the outeredge and lower in the eye).d) If the kinetic energy of the swirling air in the eye could be convertedcompletely into gravitational potential energy, how high would the airgo? (Ans: 157 m).e) In fact, the air in the eye is lifted to heights of several kilometers. Howcan you reconcile this with your answer to part d). (Ans: theatmospheric pressure decreases with height).

Qu. 4 The horizontal pipe, shown in Fig. P12.94, has a cross-sectional areaof 40 cm 2 at the wider portions and 10 cm 2 at the constriction. Water isflowing in the pipe, and the discharge from the pipe is 6 x 10 -3 m 3 /s (6Liters/s). Finda) the flow speeds at the wide and narrow portions. (Ans: 1.5 m/s and 6m/s respectively)b) the pressure difference between these portions. (Ans: 1.68 x 10 4 Pa)c) the difference in height between the mercury columns in the U-shapedtube. (12.6 cm)