--%>

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 : Hard links Explain the term hard links?

    Explain the term hard links?

  • Q : Define feasibility study Feasibility

    Feasibility study: In order to take wise investments in a market-place experiencing rising stages of risk, companies are turning to feasibility studies to find out if they must propose new products, services or commence a new business endeavor. The ma

  • Q : Dynamic model for the paper machine

    Explain and derive the Dynamic model for the paper machine headbox?

  • Q : Problem on displacement response time

    (i) Formulate the equation of motion for the system shown in Figure below. List two assumptions made in this formulation. (ii) Find the response of this system at t = 3s. The system begins with the displacement of 5 cm and velocity

  • Q : Aerospace Computational Techniques -

    Hello, I have a programming assignment that incorporates aerodynamics. I was wondering if it is possible to program the following assignment. If not, what would be the aerodynamic formulas required to do so. Thanks.

  • Q : State Concurrent Engineering Concurrent

    Concurrent Engineering has happened primarily as a result of the need to shorten product development times, but improving product quality and reducing product life-cycle costs are important considerations. Some companies have even gone to the extent o

  • 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 : Anti-Friction and Journal Bearing

    Explain difference between the Anti-Friction Bearing and the Journal Bearing?

  • 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 : Conformance to standards in product

    Conformance to standards and specifications: These are standards laid down by national and international authorities. For instance, in Canada there is the Standards Council of Canada (SCC). The United States has many standards bodies including MIL (US