2. Water flows through the pipe shown Point 2 in the diagram. It may be assumed

Question

2. Water flows through the pipe shown Point 2 in the diagram. It may be assumed that the water moves in laminar flow without friction. In the lower section of the pipe, at point 1, the pressure is P-2.00 × 104 Pa, and the pipe diameter is 6.00 cm. The higher section of the pipe is 30.0 cm higher than the lower point. The pressure in the higher section, at point 2, is P 1.00 x 104 Pa and the pipe diameter there is 2.80 cm. 30.0 cm Point 1 (a) Find the speed of flow in the lower section. (b) Find the speed of flow in the upper section. (c) Find the volume flow rate through the pipe

Explanation / Answer

a) 2 x10^4 + 1/2 ( 1000) v1^2 = 1 x 10^4 + 1/2 ( 1000) ( v2^2) + 1000(9.8) ( 0.3)

2x 10^4 + 500v1^2 = 1.294 x 10^4 + 500 v2^2 ----------------eq(1)

A1V1= A2V2

( 0.0009) ( V1) = (V2) ( 0.000196)

V1= 0.218 V2-----eq(2)

using eq(1) and eq(2)

2x 10^4 + 500( 0. 047 v2^2)= 1.294 x 10^4 + 500 v2^2

0..706 x 10^4 = 500 ( 1-0.047)v2^2

v2^2= 7060 / 476.5

v2= 3,849 m/s

v1= 0.839 m/s

flow rate= 3.14 ( 6/200)^2 ( 0.839) = 0.00237

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