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Let's begin by looking at a ow problem in which the diameter of a pipe changes along the flow path. We will need to use both the continuity equation and Bernoulli'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 Ila/in?) The cold-water pipe leading to the second-floor bathroom 5.0 m above is 1.0 cm in diameter {gure 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 required to fill a 100 L bathtub with cold water? Figure 1 of 1 I Review | Constants SOLU110N SET UP Let point 1 be at the inlet pipe and point 2 at the bathroom. The speed 1:2 of the water at the bathroom is obtained from the continuity equatiOn, A1111 = Agog. We take y1= 0 at the inlet and yz = 5.0 m at the bathroom. We are given p1 and v1; we can find 132 from Bernoulli's equation. To nd the time required to fill the bathtub, we use the volume flow-rate relationship AV/At = Av. The bathtub's volume is 100 L = 100 x 103m3. SOLVE From the continuity equation, the ow speed U2 in the bathroom is U2 = %m = %m me = 8-0 m/s- From Bernoulli's equation, the gauge pressure p2 in the bathroom is 111 $96022 - v12) - mm yl) 4.0 x 105 Pa %(1.0 x 103 kg/m3)(e4 m2 52 4.0 mz/sz) 41.0 x 103 kg/m3)(9.so m/s2)(5.o m) 3.2 x 1051):; P2 3.2 atm = 47 Ila/in.z (gauge pressure). The volume flow rate is AV/At = A2u2 = (0.50 x 102m)2(8.0 m/s) 6.3 x 10'4m3/s = 0.63 L/s. The time needed to fill the tub is 100 L/(O.63 L/s) = 160 s. REFLECT Note that when the water is turned off, the second term on the light ofthe pressure equation vanishes, and the pressure rises to 3.5 x 105 Pa. In fact, when the uid is not moving, Bernoulli's equation reduces to the pressure relationship that we derived for a fluid at rest. 7 Part A - Practice Problem: Determine the gauge pressure tor a 2.0-cmdiameter1aucet located next to the washing machine in the basement, 2.? m below where the pipe enters the house. Express your answer with the appropriate unlts. M Previous Answers Request