14_4-6 solutions - SOLUTIONS Ch. 14: 4-6 14.34. IDENTIFY:...

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SOLUTIONS – Ch. 14: 4-6 14.34. IDENTIFY: The volume flow rate is Av . SET UP: . . 3 0.750 m/s Av = 2 /4 AD π = EXECUTE: (a) . 23 0.750 m/s vD = 3 22 4(0.750 m/s ) 472 m/s (4.50 10 m) v == × . (b) must be constant, so . 2 vD 11 2 2 = 2 2 21 1 2 (472 m/s) 52.4 m/s 3 DD vv ⎛⎞ = ⎜⎟ ⎝⎠ . EVALUATE: The larger the hole, the smaller the speed of the fluid as it exits. 14.41. IDENTIFY and 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 2 0. v = Figure 14.41 Solve for 1 p and then convert this absolute pressure to gauge pressure. EXECUTE: 111 222 pg y v y v ρ ρρ ++ = Let The mains have large diameter, so 1 0, y = 2 15.0 m. y = 1 0. v Thus 12 2 . p y =+ But 2a , p p = so 32 5 1a 2 (1000 kg/m )(9.80 m/s )(15.0 m) 1.47 10 Pa. pp g y −= = = × 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 2 gh , where h is the distance of the hole below the surface of the fluid.
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