How much pressure do I need to push 5 gal/min through 3/4" hose?

Question

I know 3/4" is probably too narrow for this, but its what I have for now.

Answer 1

Disregarding friction, the pressure may be calculated this way:

Let:

Q = rate of flow = 5 gal /min = 5/(7.48 x 60) cuft/sec

c =coefficient of discharge ( assume it to be 0.8)

A = cross sectional area of hose = pi x 0.75^2/(4 x 144) sq.ft

v = velocity of discharge in ft /sec

p = pressure

w = density of water = 62.4 lbs/cuft

g = acceleration of gravity = 32ft/sec^2

Q = cAv, hence

v =Q/cA = (5/(7.48x60)/((0.8 x pi x .75^2/(4x144)) = 4.539 ft/sec

But:

p = w v^2/(2 x g) = 62.4 x (4.539)^2/(2 x 32) = 20.087 lbs/sq.ft

= 0.1395 psi

Your 3/4" hose is big enough.

Answer 2

Is there any friction?

Use Bernoulli's Equation.  Assume you have a reservior with static fluid and the hose is spilling to the atmosphere.

v1=0

p1=?

v2=QA (From continuity)

P2=0

Answer 3

That depends on a couple of things:

1.) The actual inside diameter of the hose (is it 0.72", 0.79" or something in between?  a little makes a big difference.)

2.) The "C-factor" (how smooth it is on the inside)

3.) How long it is

4.) How many bends are in the hose

5.) How sharp the bends are.

I do hydraulic calculations for a living and that isn't a simply question to answer with any accuracy unless you give a LOT more information.  If you just want a guess, I would say something in the range of 80-90psi would push 5gpm through a standard 50 foot garden hose.  Again, without more information, you just are not going to get an accurate answer.