Bernoulli applies for incompressible fluids, steady and inviscid flow, which sounds like your condition. Therefore:
P1 + .5*ρ*V1^2 + γ*z1 = P2 + .5*ρ*V2^2 + γ*z2
P = pressure
ρ = density of water
V = velocity
γ = specific weight of water
z = height
1 is an arbitrary starting point sufficiently far away from 2, the location of the hole, such that the velocity of water at point 1 is zero. The height is constant from 1 to 2, assuming horizontal pipe. You can say P2 is zero if you account for atmospheric pressure in P1. Therefore, the equation reduces to:
P1 = .5*ρ*V2^2
This does not account for friction losses at the hole.
You can relate the velocity of water to volumetric flow rate using Q=AV.
If the viscosity is significant, things get a little more complicated, but I have equations for laminar and turbulent conditions if you need it.