How to calculate flow rate and rpm of a hydraulic vane motor with restrictor installed into it 1

[Startto]

How can we calculate the flow rate and rpm of a hydraulic vane rotator/motor, if we use a steel restrictor pipe with diameter 4mm length 7.5mm. Pressure of pumped fluid is 250 bar and pressure of fluid at outlet of the motor is 25 bar?
Restrictor pipe is installed to both inlet and outlet channels inside the motor.

 

[hydtools]

You can not, given your information.

Ted

 

[Startto]

@hydtools
What all informations should be measured?
Density of oil is about 857 KG/mm3
Volume/ Capacity = 1000 cm3

 

[hydtools]

Flow rate and rpm are are related by:
Q volume per unit time = motor displacement per revolution multiplied by revolutions per unit time

cc/min = cc/rev x rpm

Ted

 

[Startto]

@hydtools
I think it should be Q(CC/min) = Displacement(Cubic centimeter)/ RPM
Correct me if I am wrong.

I get 50 RPM for inlet pressure of 200 bar.
So for 1000cm3 Q should be = 1000/50
= 20 cc/min.

After inlet the fluid goes through a reducer pipe of length 7.5mm and inner diameter of 4mm.
Now I want to cross check whether this reducer delivers a flow of 20 cc/min.
How can we calculate that?

 

[hydtools]

cc/rev x rev/min = cc/min. Rev's cancel

Ted

 

[rb1957]

do we know "displacement" ?

all we know is the pressure drop over the motor, and that the inlet and output are the same geometry.

With density and Bernoulli we can calculate the flow rate, assuming flow conditions in the inlet and outlet are the same (ie coefficient of discharge is independent of flow rate).

but rpm ??

another day in paradise, or is paradise one day closer ?

 

[hydtools]

Does Bernoulli account for work extracted by the motor?

Ted

 

[BrianPetersen]

Another thing that hasn't been stated is the output torque of the motor, and the flow characteristics ("pressure loss" - and leakage characteristics!) of the motor.

Some of the pressure will be lost across the first restrictor. Some of the pressure will be lost through the flow characteristics of the motor. Some of the pressure will be lost actually performing mechanical work showing up at the motor's output shaft. Some leakage flow will get past the motor without accomplishing anything useful. And then some more pressure will be lost across the second restrictor (which will be the same as the first one, for calculation purposes).

And on that point, some of these might be functions of the properties of the hydraulic oil. And the temperature.

You need to know everything, we've got next to nothing.

This is not simple, by the way, unless simplifying (idealising) assumptions are made ... and you had better know what those are, and whether those translate meaningfully to the real world.

 

[Startto]

@hydtools.
You were right. my mistake in interpreting the formula.
Actually the solution is
From rpm we can calculate the flow as you mentioned.
To calculate the flow from the restrictor dimension, we have to find P1 and P2 using bernoulli's equation.
Then to find flow I used Poiseuille law.

At Least that's what the solution which I had got for now.

 

[Startto]

@rb1957
Displacement 1000 CC/rev

 

[Startto]

@Brianpetersen.
Torque - 2000Nm
Leakage - 10 LPM.
From bernoulli's equation and pressure drop from restrictor is 0.5 bar.
Fluid is has viscosity co-efficient of 32 CSt
At present I don't know any simplified method to calculate the pressure drop from mechanical work.Please do share it if you know any simplified method.
weight of shaft 14 kg and vane is 0.15 kg. there is total of 8 vanes.