--%>
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 : 01 a vaccume guage connected to chamber

    a vaccume guage connected to chamber 40kpa at location where atmospheri pressure is100kpa .determine absolute pressure

    		•
  • Q : Calculate the surface area available

    You are working in a company that has developed a process to produce DNA vaccines from E.coli. After the fermentation step a lysis step is used to release the DNA from the cells resulting in a sticky mixture. You find that an aggressive cleaning solution heated to 80°C is required to

    		•
  • Q : Excitation of Modes in Fiber A

    A multimode fiber is used to couple light into a single mode fiber. Both fibers have the same total diameter. Explain the coupling. Use equations, MATLAB, etc. if necessary. If an LED is used to excite a single mode fiber, explain the coupling of light to the fiber? U

    		•
  • 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 : 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 Are you able to assist with these

    Are you able to assist with these two assignments in Arena simulation below? You can use the Basic Process instead of Blocks and Elements. An office of state license bureau has two types of arrivals. Individuals interested in purchasing new plates are characterized to have inter-arrival times dis

    		•
  • Q : Safety in Product design specification

    Safety: The specifications should state the possible abuse and misuse the product might be subjected to. Warning labels and instructions on safe operation of the product should be given. The designer can be held accountable for any accidents that migh

    		•
  • Q : Safe turbine operation For safe turbine

    For safe turbine operation how many governors are generally required and Why?

    		•
  • Q : Formation of Cavitation Explain the

    Explain the reason behind formation of the Cavitation in the Centrifugal Pump and not in the Displacement Pump?

    		•
  • Q : Product performance in Product design

    Product performance: Depending on the product, this may take many forms. Speed, loads to be withstood, number of work cycles, and intermittent or continuous working are some examples of considerations. 

    		•