Pump pressure and pipe diameter

[wasija]

I am a little confused about the pressure and hose diameter relationship. Let's say I have a pump pumping at a given pressure; I connect a hose of a certain diameter and attach a pressure gauge to the other end of the hose and get a pressure reading. Now let's say if i conduct the same experiment with a smaller diameter hose and measure the pressure. Assuming the hose length is the same and hoses are made of same material. How would the pressure reading, velocity and flow rate vary.
Thanks

 

[russ_watters]

Welcome to PF.

This is an interesting and complicated question, but starts off with an assumption that isn't necessarily true:

Let's say I have a pump pumping at a given pressure...

Pumps don't have a single pressure, they have curves:

The pressure depends on the pump but also how much restriction there is in the piping. The piping restriction is represented by a parabolic curve called the "system curve". So:

I connect a hose of a certain diameter and attach a pressure gauge to the other end of the hose and get a pressure reading. Now let's say if i conduct the same experiment with a smaller diameter hose and measure the pressure. Assuming the hose length is the same and hoses are made of same material. How would the pressure reading, velocity and flow rate vary.

See this pump curve with two system curves on it:

http://www.webbpump.com/_build/images/pump/technical-support/sect_a9_01.gif

The dark system curve represents your first scenario. The dashed curve represents your second scenario. Where the system curve meets the pump curve is what determines the flow and pressure at the pump.

Note that the shape of the pump curve and system curves can produce different results for different systems. You might have a system where you are on the high, flat part of the pump curve, so changing the system curve (by changing the pipe) may have no impact on the pressure but a big impact on flow. Or it could be the other way around.

Fuller treatment here: http://www.engineeringtoolbox.com/pump-system-curves-d_635.html

 

[256bits]

I connect a hose of a certain diameter and attach a pressure gauge to the other end of the hose and get a pressure reading

Just one comment - if the other end of the hose exits to atmosphere, and that is where your pressure gauge is attached, then you should read nearly the same pressure regardless of size of hose. The pressure head at exit is always Patm.
Put your gauge closer to the pump end.