An underground pipe carries water of density 1000 kg/m^3 to a fountain at ground

Question

An underground pipe carries water of density 1000 kg/m^3 to a fountain at ground level. At point A, 0.50 m below ground level, the pipe has a cross-sectional area of 1.0 x 10^-4 m^2. At ground level the pipe has a cross-sectional area of 0.5 x 10^-4 m2. The water leaves the pipe at point B at a speed of 8.2 m/s. a) Calculate the speed of the water in the pipe at point A b) Calculate the absolute water pressure in the pipe at point A c) Calculate the minimum height above the ground that the water reaches upon leaving the pipe vertically at ground level, assuming air resistance is negligible. d) Calculate the horizontal distance from the pipe that is reached by water exiting the pipe at 60 degrees C from the ground level, assuming air resistance is negligible.

Explanation / Answer

Q=Av
a) Q=4.1*10^-4 m^3/s
Q will be same at both points , so v at A = 4.1/1 = 4.1 m/s
b) for absolute pressure (P-gh-101000)Aavg =dm/dt *v

dm/dt = 0.41 kg/s

so P=128.313 kPa

c) v2 =2gh

h=3.43m

d) this is the question for projectile motion where R is given by v2 sin2/g = 5.941m

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