Viscous Drag on a spinning shaft

  1. I am designing a test rig for my company to test seals.
    What i have is a shaft spinning in a fluid column that is pressurized to 30 bar. The shaft is spun by a motor and i am currently trying to figure out what motor i should select. The fluid is a C4 SAE 30 Oil, quite viscous actually. My intuition tells there will be hydrodynamic friction due to the shafts rotation and hydrostatic forces due to 30 bar pressure creating more friction. Can you guys tell me how to figure this out?

    In brief the question is -
    - 80 mm shaft spinning at 3000 RPM inside a 100mm cylindrical fluid column
    - The fluid is SAE 30 Oil
    - The oil is pressurized to 30 bar
    What is the frictional torque on the shaft ? What is the Power and Torque required by my prime mover (P = Tw anyway ;) )

    Thanks in advance. Any help will be appreciated a lot bros :)
  2. jcsd
  3. What's the viscosity of the oil? Does it vary with shear rate? What's the length of the shaft? You may also need to consider whether viscous heating is going to be a factor. You can get an upper bound to the torque by neglecting the viscous heating. Is that acceptable?


    The viscosity of the oil is given in that documentation. It varies with temperature, but i dont know whether it will vary with shear rate. The length of shaft is 120mm (inside fluid column). You can neglect viscous heating because when the motor starts the temperature of oil is around room temperature (So like 25-30 C) and the motor has to overcome the torque at that time also.

    Thanks a lot if you can tell me how :)
  5. The velocity of the inner cylinder is V=ωRi, where ω is the angular velocity and Ri is the radius of the inner cylinder. The shear rate in the gap between the cylinders is γ=V/(Ro-Ri), where Ro is the radius of the outer cylinder. The shear stress at the wall of the inner cylinder is τ=ηγ, where η is the viscosity. The torque on the inner cylinder is T=2πR2Lτ. The power is P=TV.

    (The viscosity is going to be higher at 25C than at 100 C.)

  6. Okay. You havent considered the effect of pressure in the viscous drag. Wont 30 bar pressure create some effect?
  7. boneh3ad

    boneh3ad 1,684
    Science Advisor
    Gold Member

    No. Pressure will not directly lead to any additional shear stress since it will act only in the direction perpendicular to a given face (i.e. toward the shaft center). The only way it would have an effect is if changing pressure affects the temperature of your oil, and you have already accounted for temperature. Otherwise, the only other way it could affect viscous drag is if pressure affected the viscosity of your oil. I won't say that never happens, but I will say I have never heard of such a fluid.
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