Water is flowing in the pipe shown in the figure below, with the 7.80-cm diamete

Question

Water is flowing in the pipe shown in the figure below, with the 7.80-cm diameter at point 1 tapering to 3.40 cm at point 2, located y 12.5 cm below point 1. The water pressure at point 1 is 3.20 x 104 Pa and decreases by 50% a point 2. Assume steady, ideal flow. What is the speed of the water at the following points (a) point 1 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s (b) point 2 5.78 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s Need Help? Read It

Explanation / Answer

P1 = 3.2 *10^4 Pa

P2 = 0.50 *3.2 *10^4

let the speed of flow is v1 and v2

Using continuity equation

7.8^2 * pi * v1 = 3.4^2 * pi * v2 -----(1)

Using Bernoull's equation

3.2 *10^4 + 0.5 * 1000 * v1^2 + 1000 * 9.8 * 0.125 = 0.50 * 3.2 *10^4 + 0.5 * 1000 * v2^2 ---(2)

solving 1 and 2

v1 = 1.13 m/s

v2 = 5.98 m/s

the speed of flow at point 1 is 1.13 m/s

b) the speed of flow at the point 2 is 5.98 m/s

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