--%>
Assignment Help - homework help

Problem on mechanical efficiency of the pump

The oil pump is drawing 25 kW of electric power while pumping oil with ρ = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are of 8 cm and 12 cm, respectively. When the pressure rise of oil in the pump is measured to be 250 kPa and the motor efficiency is 90%, then find out the mechanical efficiency of the pump. Taking kinetic energy correction factor to be 1.05.

598_mechanical eff.jpg

E

Expert

Verified

Given:

Inlet Dia, Di = 8 cm = 8 x 10-2 m
Outlet Dia, Do = 12cm = 12 x10-2m

Density of oil,  δ = 80Kg /m3

Flow rate Q = 0.1 m3/s

Pressure rise = 250KPa = 250 x10-3 Pa

Power supplied to the pump = 25Kw = 25 x 10-3 w

Motor efficiency = .90

Kinetic energy correction factor, α= 1.05

Inlet area Ai= Π/4 x D12=-Π/4 x (8 x 10-2)2 = 0.0804 m2
Outlet area A0= Π/4 x D02 = Π/4 x (12 x10-2)2= 0.1809 m2

Average evolution 
Vi = Q/Ai = 0.1/ 0.804 = 1.1235 m/s
V0 = Q/A0 = 0.1/ 0.1809 = 0.5526 m/s

A note of kinetic energy correction factor

K. E correction factor, α = (K. E /See based on actual velocity) / (K. E / See based on average velocity)

The factor α is used when the flow is viscous.

Applying Bernoulli’s equation at the inlet (i) i outlet (0) of the pump.

Pi/ δg + α1 Vi2/ 2g +zi + HP= P0 /δg +α2 Vo2/2g + Z0 + Hf .

Given  αi= α2= α= 1.05     (Z0 –Zi is considered negligible)
HP = head added by the pump
Hf = head loss due to friction

H= HP – Hf = P0–Pi / δg + α ( V02-V12)/ 2g
    = 250 x 103 / 1000 x 9.81 + 1.05 / 2 x 9.81 (0.55262  - 1.2435)
    = 25.42 m

Power of the pump PP= δg QH
            = 1000 x9.81x 0.1 25.42
            = 24934.85 w
            = 24.934Kw

Mechanical efficiency of the pump:

Case (1)  ηm = power output/power input = 24.934/ 25 = 99%
Case (2)  if the  motor is to get 25Kw  considering its efficiency  the supply should be of 25/ 0.9 KW

ηm = 24.934/ (25/0.9) = 89.67%

   Related Questions in Mechanical Engineering

  • Q : Carburetion A carburetor's primary

    A carburetor's primary function is to mix proper proportions is?

    		•
  • Q : Problem on mechanical efficiency of the

    The oil pump is drawing 25 kW of electric power while pumping oil with ρ = 860 kg/m3 at a rate of 0.1 m3/s. The inlet and outlet diameters of the pipe are of 8 cm and 12 cm, respectively. When the pressure rise of oil in the pump is measured to be 250 k

    		•
  • Q : Problem on steam turbine 1) A steam

    1) A steam turbine takes in saturated steam at 300oc and outputs steam at 4 bar. When the efficiency of the turbine is 65%, Evaluate: a.  The final composition (vapor vs. liquid) of outgoing steam.b.  The

    		•
  • Q : Working environment in Product design

    Working environment: The conditions under which the product is likely to be used, stored, and transported must be specified. The product may have to operate in conditions of extreme temperature, be subject to vibration, radiation; these conditions wil

    		•
  • Q : Problem on turbulent flow The

    The approximate equation for the velocity distribution in a rectangular channel with the turbulent flow is 655_turbulent flow.jpg

    Q : What is machine shop Machine shop : A

    Machine shop: A facility which employs machines to fabricate devices from stock raw materials or to change mechanisms based on given specifications. Also termed as "Back" Shops. The general machines in a machine sh

    		•
  • Q : Problem on Ideal gas process A) Air at

    A) Air at 4MPa and 3000C enters a will insulated turbine operating at steady state with negligible velocity. The air expands to an exit pressure of 100KPa. The exit velocity and temperature are 90 m/s and 1000C respectively. The diameter of the e

    		•
  • Q : What is wrap-around Wrap-around : The

    Wrap-around: The main aim of a wrap-a-round is to make a straight line about a pipe to help in cutting the pipe to its appropriate length. It is employed mostly as a straight edge or a template.   

    		•
  • Q : Difference between pressure vessel &

    Difference between pressure vessel & column: The Pressure vessels (cylinder or tank) are utilized to store fluids under pressure. If the pressure vessel are design in the form of column to separate the gas at u

    		•
  • Q : Change of power in flow of kinetic

    Air at 20 m/s, 260 K, 75 kPa with 5 kg/s flows into a jet engine and it flows out at 500 m/s, 800 K, 75 kPa. What is the change (power) in flow of kinetic energy?

    		•