I\'m designing a simple hydraulic system. The pump drives the fluid to a hydraul

Question

I'm designing a simple hydraulic system. The pump drives the fluid to a hydraulic motor, with a given Torque of 200NM, and RPM of 2800. I chose the pressure of the system to be 100bar. From this, I found the motor's capacity to be 0.0002m^3. The flowrate is (9.33*10^-3 m^3/s). I need to find the flow velocity of the fluid from this information. What I need to use it for is to calculate the inner diameter of the system pipes. By dividing flowrate and the flow velocity, I find the pipe area, and from this I can find the diameter.

Explanation / Answer

Power P = 2 x Pie x N x T /60

= 2 x 3.14 x 2800 x 200 / 60

= 59363 w

head H = P / rho x g

1 x 10^5 / 1000 x 9.81

= 10.19m

Q = Area x velocity

   = pie / 4 x d^2 x velocity

9.33 x 10 ^-3 = 3.14/4 x d^2 x V

let the efficiency of power transmission = 90 %

efficiency = H - hf / H = 0.9

0.9 = 10.19 - hf / 10.19

10.16 x 0.9 = 10.19 - hf

9.17= 10.19 - hf

hf = 10.19 - 9.17 =1.02 m

hf = 4 x f xL x V^2 / d x 2 x g

1.02 = 4 x 0.0065 x 2000x V^2 / d x 2 x g

but Q = Area x velocity

= pie / 4 x d^2 x V

9.33 x 10^-3 = 3.14 x d^2 x v / 4

V = 0.011 /d^2

1.02 = 4 x 0.0065 x 2000 x 0.0011^2 / d x 2 x 9.81 x d^4

diameter d = 0.13338 m assumed friction factor f - 0.0065 and length of pipe = 2000 m

velocity V = 0.011 / 0.13338^2

= 7 m/s

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