A pump fitted with 50mm bore ball bearings uses an oil whose viscosity ranges from 100cSt at cold pump start-up to 7.5Cst when running at maximum speed and load. If these viscosities are the safe limits for the oil, specify the maximum start-up speed and the maximum running speed you would recommend for the pump.

Answer 1

Given that the the bore diameterof the ball bearing=50mm
At cold start-up the viscosity of oil= 100cST = 100 centistokes= 100 mm2/sec
At maximum speed condition viscosity of oil =7.5 cST= 7.5 centistokes= 7.5mm2/sec
From the viscosity formula we know that= τ = μ dc / dy
where
τ = shearing stress (N/m2)
μ = dynamic viscosity (N s/m2)
dc = unit velocity (m/s)
dy = unit distance between layers (m)
Lets assume the shearing stress be 1kpa.
So,from the 1st condition we get, velocity=Shear stress*unit distance/dynamic viscosity
So,the maximum start up speed is=1000*50/100 =500mm/sec
And, Maximum running speed will be = 1000*50/7.5 =6666.6667mm/sec