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
Pressure head (¥÷) = 7m
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:
Pressure=press. head*(density*gravity)
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.
To find the force exerted by the oil on the bend, we need to calculate the force due to the oil flow and the force due to the oil pressure.
First, let's calculate the mass flow rate of the oil. We can find this by multiplying the oil density (0.79 x 10^3 kg/m^3) by the volumetric flow rate (1.7 m^3/s):
Mass flow rate = 0.79 x 10^3 kg/m^3 * 1.7 m^3/s
Mass flow rate = 1343 kg/s
Next, let's calculate the velocity of the oil in the pipe. We can do this using the volumetric flow rate and the pipe diameter:
Velocity = Volumetric flow rate / (π * (pipe diameter/2)^2)
Velocity = 1.7 m^3/s / (π * (0.45/2)^2)
Velocity = 10.69 m/s
Now, let's calculate the force (F1) on the bend due to the oil flow. This can be found by multiplying the mass flow rate by the velocity:
F1 = Mass flow rate * Velocity
F1 = 1343 kg/s * 10.69 m/s
F1 = 14356 kg m/s^2 or 14.356 kN
Next, let's calculate the force (F2) due to the oil pressure. We can find the pressure using the pressure head and the oil density:
Pressure = Pressure head * (density * gravity)
Pressure = 7 m * (0.79 x 10^3 kg/m^3 * 9.81 m/s^2)
Pressure = 54249 kg m/s^2
To calculate the force, we multiply the pressure by the cross-sectional area of the pipe:
F2 = Pressure * Area
F2 = 54249 kg m/s^2 * (π * (0.45/2)^2)
F2 = 8627 kg m/s^2 or 8.627 kN
Finally, the total force (Ft) acting on the elbow is the sum of F1 and F2:
Ft = F1 + F2
Ft = 14.356 kN + 8.627 kN
Ft = 22.983 kN
Therefore, the force exerted by the oil on the bend is approximately 22.983 kN.