Physics

Lubricating oil, with a relative density of 0.79, flows around a 90¨¬ bend. The pipe diameter is 0.45m, and the oil has a pressure head of 7m and the flow is 1.7m3/s. Find the force exerted by the oil on the bend.

Oil density = 0.79 X 103
Volumetric mass flow rate = 1.7 m3/s
Pipe diameter = 0.45 m
Oil mass flow=density*Vol/sec
Mass flow=0.79X10^3*1.7
Mass flow=1343kg/sec

Oil velocity in the pipe:
Vel.*pir^2=1.7m^3/sec
vel.=1.7/pi*(0.45/2)^2
vel of oil=10.69m/s

Force(F1) on the bend due to oil flow:
F1=Oil mass flow*Oil velocity
F1=1343*10.69
F1=14356kgm/s^2 or 14.356kN

Force(F2) due to oil pressure:
p=7m*0.79X10^3kg/m^3*9.81m/s^2
p=54249kg/ms^2
F2=pA
F2=54249kg/ms^2*(0.7854X0.45^2)
F2=8627kgm/s^2 or 8.627kN

Total Force(Ft) acting on elbow:
Ft=F1+F2
Ft=14.3456kN+8.627kN
Ft=22.983kN (ans.)

Thanks for taking a look.

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