Calculate Efficiency Loss of a Leak in a Hydraulic Cylinder

I am trying to figure out what the efficiency loss of a leaking hydraulic cylinder is. This master's thesis found that a controllable pitch propeller (essentially a hydraulic cylinder inside a rotating shaft to control the pitch of the propeller) had external leakage of 0.5 ltr/min at 40 bar and internal leakage of 3 ltr/min at 100 bar. I was wondering if it would be possible to convert these numbers into a rough efficiency loss?

I have been google searching for days to try to find a reference to indicate how to make this calculation. I also went all out and went to a local university library to use Engineering Village -- hoping to find some paper that did an analogous study but couldn't find much to help.

This seems relevant but not sure how to use it: Losses through holes drilled in a pipe

• What would you base the efficiency on? engine power input? Air or fluid moved? Blade Positioning error? Peak hydraulic fluid flow? Jan 23 '19 at 5:47
• Engine power input Jan 23 '19 at 15:17

The efficiency is a dimensionless quantity and is calculated by power output devided by power input.

I hope you have the value of your power input? But you can also calculate it with the following formula. The left one is for your (electro-)motor which is convertible in your hydraulic pump.

$$P_{mechanical}=M[Nm]*2*n[1/sec]*\pi=p[bar]*Q[l/min]=P_{hydraulic}$$

There are three (main-)possibilities to get some energy loss in your system:

• the mechanical one caused by friction in your pump, motor, valves … - $$P_{loss-mechanical} [W]$$
• the pressure one caused by perfusion-resistance of the elements in your hydraulic system, e.g. in your piping – $$P_{loss-\Delta p} [W]$$
• the volumetric one caused by leakage in your hydraulic system – $$P_{loss-volumetric} [W]$$

The volumetric loss is your issue - mentioned by the two leakage (internal and external).

$$P_{l- vol} [W]= \Sigma (p[bar]*Q[l/min])=10^5*40bar*1/60000*0,5l/min + 10^5*100bar*1/60000*3l/min=533,33 W$$

Note the $$10^5$$ and the $$1/60000$$ are values because of the different units…

Now the equation for efficiency:

$$n= P_{output}/P_{input}=(P_{input}-\Sigma(P_{loss}))/P_{input}=(P_{input}-P_{l- vol})/P_{input}=(P_{input}-533,33 W)/P_{input}$$