Calculate pressure of pumped liquid

[madmike159]

I have a enclosed system for cooling bearing housings with oil. I need to calculate the rough pressure that will be produced when the oil pump is switched on. The oil will be pumped from a small tank, through the system and back into the tank.

Pipe diameter = 10.8mm
Pipe length = aprox 2m
Flow rate = 250L/s
Viscosity (this is where I get confused about Kinematic vs Dynamic)

I am stuck on how to even get started on this. Is there a simple equation/rule of thumb that would allow me to get a rough value?

 

[SteamKing]

You'll need to find out more information about your pump. At the minimum, you'll need to know the output head the pump is capable of producing.

 

[madmike159]

What do you mean by output head?

 

[Chestermiller]

You are trying to calculate the pressure drop for flow of a fluid through a pipe. You can look up the equations for this in Mechanical engineers Handbook, Chemical Engineers Handbook, or on the internet.

 

[SteamKing]

What do you mean by output head?

A pump works by changing the pressure of the fluid it is pumping. The output head refers to the amount of pressure the pump is capable of producing.

See: http://en.wikipedia.org/wiki/Pump

under the section 'Laraib Pumping Power' at the bottom of the article.

 

[Baluncore]

http://en.wikipedia.org/wiki/Darcy–Weisbach_equation

 

[Chestermiller]

http://en.wikipedia.org/wiki/Darcy–Weisbach_equation

The key to using this reference is to get the friction factor f, which is a function of the Reynolds number Re. You need to first calculate the Reynolds number, and then check to determine whether it is above or below the critical value for transition to turbulent flow (2100). In your case, it is almost certainly above the critical value. You then use the relationship between f and Re that is applicable to turbulent flow. This relationship can be found in the references I cited in my earlier post.

Chet

 

[madmike159]

Thanks guys. I had already found the Hagen-Poiseuille Equation, but I used the flow rate incorrectly (m^3/h rather than m^3/s). I now have a reasonable answer and know a limit of the size of pipe I should use.

 

[Chestermiller]

Thanks guys. I had already found the Hagen-Poiseuille Equation, but I used the flow rate incorrectly (m^3/h rather than m^3/s). I now have a reasonable answer and know a limit of the size of pipe I should use.

Don't forget that Hagen-Poiseuille applies only to laminar flow (Re<2100). If the reynolds number is higher than this, you need to use the turbulent flow correlation for the friction factor. Otherwise, you will be underestimating the pressure drop. So, check the Re.

Chet

 

[Baluncore]

Fundamentally, a cooling system should be operating at the lowest pressure possible that achives the required flow. If the flow is limited by pipe size then power will be wasted moving the oil through the tube. That will heat the oil which makes cooling the gearbox more difficult.

I think the OP may have been based on assumed data. If 250 L/s is required to achieve the required cooling then the 10.8mm pipe diameter is far too small to be in laminar flow.

There are nomographs for deciding the pipe diameter needed in hydraulic applications.
See for example; http://www.ryco.com.au/index.php?id=196
This shows you need something closer to a 50mm diameter pipe for that flow rate.

Your 10.8 mm tube would support only 25 L/s.

 

[Baluncore]

Sorry madmike159,
I just found your intermediate post with the corrected flow reduction by a factor of 3600 = 70 mL/s.

 

[madmike159]

Don't forget that Hagen-Poiseuille applies only to laminar flow (Re<2100). If the reynolds number is higher than this, you need to use the turbulent flow correlation for the friction factor. Otherwise, you will be underestimating the pressure drop. So, check the Re.

Chet

Thanks, I didn't think to check the Reynolds number. As Baluncore said, my flow rate is far to high which explains some higher than expected oil temperatures. I won't be blindly choosing the first pump I find next time.

 

[madmike159]

Your 10.8 mm tube would support only 25 L/s.

Just realized my OP was incorrect. The pump is rated to 250L/h not L/s...