The torque T required to rotate a disk of diameter D with angular velocity ω in a fluid is a function of the density ρ and the viscosity µ of the fluid (torque has units of work). (a) Find a nondimensional relationship between these quantities. (b) Calculate the angular velocity and the torque required to drive a 750 mm diameter disc rotating in air if it requires a torque of 1.2 Nm to rotate a similar disc of 230 mm diameter in water at a corresponding speed of 1500 rpm. Assume the temperature is 15°C.
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
The torque T required to rotate a disk of diameter D with
(a) Find a nondimensional relationship between these quantities.
(b) Calculate the angular velocity and the torque required to drive a 750 mm diameter disc rotating in air if it requires a torque of 1.2 Nm to rotate a similar disc of 230 mm diameter in water at a corresponding speed of 1500 rpm. Assume the temperature is 15°C.
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