A fountain with an opening of radius 0.016 m shoots a stream of water vertically

Question

A fountain with an opening of radius 0.016 m shoots a stream of water vertically from ground level at 6.7 m/s. The density of water is 1020 kg/m^3. (a) Calculate the volume rate of flow of water. (b) The fountain is fed by a pipe that at one point has a radius of 0.035 m and is 2.2 m below the fountains opening. Calculate the absolute pressure in the pipe at this point. (c) The fountain owner wants to launch the water 3.3 m into the air with the same volume flow rate. A nozzle can be attached to change the size of the opening. Calculate the radius needed on this new nozzle.

Explanation / Answer

a) Volume Flow Rate = F =
= v*A
= (6.7)*(Pi*(0.016)^2)
= 0.00539 m^3/sec

b) (v_pipe)*(A_pipe) = (v_pipe)*(Pi*(0.035)^2) = F = 0.005388
(v_pipe) = 1.4 m/sec
(P_pipe) =
= (101325) + (1/2)**v^2 - (1/2)**(v_pipe)^2 + *g*h - *g*(0)
= (101325) + (1/2)*(1000)*(6.7)^2 - (1/2)*(1000)*(1.4)^2 + (1000)*(9.8)*(2.2)
= 144372 Pa

c) ) (1/2)**v^2 = *g*h
v = Sqrt[ 2*g*h ]
v = Sqrt[ 2*(9.81)*(3.3) ]
v = 8.046 m/sec
Volume Flow Rate = F = 0.005388 =
= v*A
= (8.046)*(Pi*(R )^2)
R = 0.0146 meters

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