Viscous Drag on a spinning shaft

In summary, the speaker is designing a test rig for their company to test seals. They have a shaft spinning in a pressurized fluid column and are trying to figure out what motor to select. The fluid is viscous and pressurized to 30 bar. The speaker is also asking for help in calculating the frictional torque, power, and torque required for the motor. They provide additional information such as the size and speed of the shaft, the type of oil being used, and the length of the shaft. The conversation also touches on factors such as the viscosity of the oil and whether pressure will affect viscous drag.
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 :)

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?

Chet

Chestermiller said:
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?

Chet

The viscosity of the oil is given in that documentation. It varies with temperature, but i don't 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 :)

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.)

Chet

Okay. You haven't considered the effect of pressure in the viscous drag. Wont 30 bar pressure create some effect?

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.

1. What is viscous drag on a spinning shaft?

Viscous drag on a spinning shaft is the resistance force that acts against the motion of the shaft due to the fluid it is spinning in. This force is caused by the friction between the fluid and the surface of the shaft.

2. How is viscous drag calculated?

Viscous drag on a spinning shaft can be calculated using the formula F = μAv, where F is the drag force, μ is the dynamic viscosity of the fluid, A is the surface area of the shaft, and v is the velocity of the fluid relative to the shaft.

3. What factors can affect the magnitude of viscous drag on a spinning shaft?

The magnitude of viscous drag on a spinning shaft can be affected by factors such as the viscosity of the fluid, the surface roughness of the shaft, the velocity of the fluid, and the diameter and length of the shaft.

4. How can viscous drag on a spinning shaft be reduced?

Viscous drag on a spinning shaft can be reduced by using a more streamlined shape for the shaft, reducing the surface roughness, or using a less viscous fluid.

5. What are some real-world applications of studying viscous drag on spinning shafts?

The study of viscous drag on spinning shafts has many practical applications, such as in the design of turbines and propellers for efficient fluid flow, in the development of more efficient pumps and compressors, and in the optimization of industrial processes such as mixing and stirring. It is also important in understanding the behavior of fluids in pipes and channels, which is crucial for the transportation of liquids and gases in industries such as oil and gas, chemical, and water treatment.

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