SOLUTIONS – Ch. 14: 4-6 14.34.IDENTIFY:The volume flow rate is Av. SET UP:. . 30.750 m/sAv=2/4ADπ=EXECUTE:(a). 230.750 m/svD=3224(0.750 m/s )472 m/s(4.50 10 m)v−==×. (b)must be constant, so . 2vD112 2=222112(472 m/s)52.4 m/s3DDvv⎛⎞=⎜⎟⎝⎠. EVALUATE:The larger the hole, the smaller the speed of the fluid as it exits. 14.41.IDENTIFYand SET UP:Apply Bernoulli’s equation to points 1 and 2 as shown in Figure 14.41. Point 1 is in the mains and point 2 is at the maximum height reached by the stream, so 20.v=Figure 14.41 Solve for 1pand then convert this absolute pressure to gauge pressure. EXECUTE:111222pgyvyvρρρ++=Let The mains have large diameter, so 10,y=215.0 m.y=10.v≈Thus 122.py=+But 2a,pp=so 3251a2(1000 kg/m )(9.80 m/s )(15.0 m)1.47 10 Pa.pp gy−=== ×EVALUATE:This is the gauge pressure at the bottom of a column of water 15.0 m high. 14.89.IDENTIFY:Apply Bernoulli’s equation and the equation of continuity. SET UP:Example 14.8 says the speed of efflux is 2gh, where his the distance of the hole below the surface of the fluid.
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