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Answer :
The volume rate of flow of water from the 1.70-cm-diameter faucet with a pressure head of 14.0 m is approximately 1.78 x 10^-5 m^3/s
r = d/2 = 0.85 cm = 0.0085 m
P = rho * g * h = 1000 kg/m^3 * 9.81 m/s^2 * 14.0 m = 137340 Pa
now,
P + 1/2 * rho * v1^2 = constant
A1 * v1 = A2 * v2 = pi * r^2 * v2
v2 = 0
P + 1/2 * rho * v1^2 = P0
v1 = sqrt((P0 - P)/(1/2 * rho))
where P0 is the atmospheric pressure (101325 Pa) and rho is the density of water (1000 kg/m^3).
putting in the values:
v1 = sqrt((101325 Pa - 137340 Pa)/(1/2 * 1000 kg/m^3))
v1 = 7.82 m/s
Finally, we can use the formula for the volume rate of flow (Q):
Q = A1 * v1
Q = pi * r^2 * v1
Q = pi * (0.0085 m)^2 * 7.82 m/s
Q = 1.78 x 10^-5 m^3/s
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