Is there a simple relationship between water flow, pipe diameter, and pressure?

Answer 1

The velocity head is the vertical distance that a body would have to fall to acquire a given velocity = v. It corresponds to the static or pressure head which would cause that velocity = velocity head = hv

hv = 0.00259 x (gpm)^2/(d)^4

d = inside diameter of the pipe in inches
gpm = gallons per minute flow rate of liquid
hv = pressure in feet of liquid that will cause the gpm flow rate
in a pipe with an inside diameter = d
For water, 1 psi = 2.31 feet of liquid head.

Answer 2

Yes, it is called continuity equation. Q = A V
Where Q = Flow, A = cross sectional area (related to Diameter) and V = velocity.
If Diameter increase, Area increases and to keep the Q constant V decreases. If diameter decreases, area decreases and to keep the Q constant V increases. This is the reason when garden hose is squeezes at opening with thumb or something, water jet reaches farther.

Answer 3

I'm wondering if the simple answer is that it is an exponential relationship between diameter and flow rate?

Answer 4

the regular bernoulli equation
all eqations are taken from it
they are all bad