--%>
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 : Radial bearings Explain the importance

    Explain the importance to remember about the radial bearings?

    		•
  • Q : Problem on head loss The pump

    The pump illustrated in the figure adds 20 kW of power to the flowing water. The only vital loss is that which takes place across the filter at the inlet of the pump. Find out the head loss for this filter. Note that the gage pressure upstream of the filter is negativ

    		•
  • Q : Problem on magnitude of force A

    A horizontal pipe of dimension 540 mm diameter carrying 0.6 m3/s splits into two horizontal pipes of 300 mm diameter with 60% of the flow and another of 150 mm diameter with 40% of the flow. Find out the magnitude and direction of the force

  • Q : What is critical speed What is critical

    What is critical speed?

    		•
  • Q : Bearing number ti Diameter of inner and

    Specify how the Bearing number ti Diameter of the inner and outer can be calculated?

    		•
  • Q : Mode Superposition Method Define Mode

    Define Mode Superposition Method in brief?

    		•
  • Q : MECHANICAL ENGINEERING DESIGN KINDLY

    KINDLY SEND ME MATERIAL ON "MULTISTAGE SPUR GEAR DESIGN OPTIMISATION USING RAY DIAGRAMS"

    		•
  • Q : Ergonomics in product design

    Ergonomics: This is concerned with how easy (comfort, complexity) the product is to use by the targeted market. Physical human dimensions must be considered when designing the driver's seating, instruments, and controls in a car. Slight variations bet

    		•
  • 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 : Arena simulation Are you able to modify

    Are you able to modify the attached [HW4-4-1sawModifiedInstructorTemplate] with the information below for this assignment? Modify the attached exercise by adding agent breaks. The 16 hours are divided into two 8-hour shifts. Agent

    		•