pp30 Practice Problem 13.9 Practice Problem 13.9 Let\'s begin by looking at a fl
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pp30 Practice Problem 13.9 Practice Problem 13.9 Let's begin by looking at a flow problem in which the diameter of a pipe changes along the fow path. We will need to use both the continuity equation and Bemoulli's equation for this problem. Water enters a house through a pipe with an inside diameter of 2.0 cm at a gauge pressure of 4.0 x 105 Pa (about 4 atm, or 60 lb/in.2) The cold-water pipe leading to the second-Moor 5.0 m above is 1.0 cm in diameter (Figure 1). Find the flow speed and gauge pressure in the bathroom when the flow speed at the inlet pipe is 2.0 m/s. How much time would be Figure 1 of 1 Hot water tmk an ppe) previous l 2 of 2 l retum to assignmen SOLUTION SET UP Let point 1 be at the inlet and at the bathroom. The speed v2 of the water at the bathroom is obtained from the continuity equation, A1v1 A202. We take vi 0 at the inlet and V2 5.0 m at the bathroom. We are given ph and we can find ph from Bemouws To find the time required to fill the bathtub, we use the volume flow rate relationship AV/At Av. The bathtub's volume is 100L 100 x 10 m3 SOLVE From the continuity equation, the flow speed in the bathroom is *(1.0 em)? (2.0 m/s) 8.0 m/s 2 *(0.50 cm From Bernoull's equation, the gauge pressure p2 in the bathroom is 4.0 x 105 Pa -1 (1.0 x 103 kg/m (64 m3/s 40 m2/s -(1.0 x 103 kg/m3)(9.80 m/s (5.0 m) 3.2 x 105 Pa. (gauge pressure) 47 lb/in. 3.2 atm The volume flow rate is AV/At A2th m(0.50 x 10-2 m) (8.0 m/s) 6.3 x 10 4 m3/s 0.63 L/s The time needed to fill the tub is 100 L/(0.63 L/s) 160x REFLECTNote that when the water is turned off, the second term on the right of the pressure equation vanishes, and the pressure rises to 3.5 x 103 Pa. In fact, when the fuid is not Bernoullis equation reduces to the pressure relationship that we derived for a fluid at restExplanation / Answer
Mass flow rate is constant.
Hence pressure at the faucet = P0 + rho * g * h = 10^5 + 10^3 * 10* 2.4 = 124000 N/m^2
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