Question

A 280-km-long pipeline connects two pumping stations. If 0.56m3/s are to be pumped through a 0.62-m-diameter line, the discharge station is 250m lower in elevation than the upstream station, and the discharge pressure is to be maintained at300,000Pa,determinethepowerrequiredtopumptheoil.The oilhas akinematic viscosity of4.510"6m2/s anda density of 810kg/m3.Thepipeisconstructedofcommercialsteel.Theinlet pressure may be taken as atmospheric.

Answer 1

Answer:

Explanation:

(a) we take the free surface of the lake to point 1 and the free surfaces of the storage tank to point 2. We also take the lake surface as the reference level (z1= 0), and thus the potential energy at points 1and 2 are pe1= 0 and pe2= gz2. The flow energy at both points is zero since both 1 and 2 are open to the atmosphere (P1= P2= Paytm). Further, the kinetic energy both points is zero (ke1= ke2= 0) since the water at both locations is essentially stationary. The mass flow rate of water and its potential energy at point 2 kg/s70/s)m070.0)(kg/m1000(33===V&&rmkJ/kg196.0/sm1000kJ/kg1m)20)(m/s(9.8122222===gzpe

Then the rate of increase of the mechanical energy of water becomes kW13.7kJ/kg)6kg/s)(0.1970()0()(22inmech,outreach,fluid mech,===-=-=DpempemeemE&&&&The overall efficiency of the combined pump-motor unit is determined from its definition,67.2%or 0.672

NB:

Please check the attached file for clearer work.