what is the discharged rate of water leaking at a 4 inches diameter pvc pipe with pressure of 35 psi and a leak hole of 5 mm in diameter
The diameter of the hole (d = 5*10^-3 m) matters, but the pipe diameter does not*. The velocity of water leaving the hole is (from Bernolli's equation)
V = sqrt(2*deltaP/density)
deltaP= 35 psi = 2.24*10^5 N/m^2
density = 1.00^10^3 kg/m^3
V = 21.2 m/s
Discharge rate = V*Ahole
= 21.2 m/s*(pi/4)d^2
= 4.16*10^-4 m^3/s
= 416 cm^3/s
*We have neglected the velocity of water in the manifold, since the pipe diameter is large compared to that of the hole.