Mechanical engineering help with fluids

[apamnani1]

Hi people!

I have been doing some fluid questions and got stuck ont he following two;


1) A Casson plastic fluid is subjected to a shear force of 5.5 Pa. If the fluid obeys a law of the form T =1.5 +0.2^0.45u, determine the shear rate and apparent viscosity under these conditions

2) Oil of dynamic viscosity 0.12 Nsm-2 is used to lubricate the space between the plain journal bearing with the shaft. The shaft and bearing are concentric and the space between them is filled with an oil of dynamic viscosity of 0.15Nsm^-2.

Determine the torque required to overcome viscous resistance and the power loss when the shaft is rotating at a speed of 3000rpm.


Any help would be amazing!

Cheers

 

[lippyka]

, Kev.For the first question, the shear rate can be calculated using the equation u = (T - 1.5)/0.2^0.45, where T is the shear stress (5.5 Pa). Thus, the shear rate is equal to 4.9 s-1. The apparent viscosity can then be calculated using the equation η_a = T/u, where η_a is the apparent viscosity and u is the shear rate (4.9 s-1). Therefore, the apparent viscosity is equal to 1.12 Pa s. For the second question, the torque required to overcome viscous resistance can be calculated using the equation T = 2πnηL, where n is the rotational speed (3000 rpm), η is the dynamic viscosity of the oil (0.12 Nsm-2), and L is the length of the shaft in m. The power loss can then be calculated using the equation P = Tω, where P is the power loss, T is the torque, and ω is the angular velocity (ω = 2πn = 18,849.36 rad/s).