Question

A piston head inside an engine is allowed to vertically free fall. The cylinder diameter is 0.5 in, and the piston head has a diameter of 0.45 in and a mass of 0.8 lbm. A thin layer of unused engine oil separates the head from the piston. Determine the percentage increase in the speed at which the head falls if the temperature of the oil increases from 75 °F to 200 oF. cylinder head engine oil

Answer 1

First of all we have to take some assumption n_1 at 75 degree E rightdoublearrow 0.17N s/m^2 [SAE - 20] n_2 at 200 degree F rightdoublearrow 0.0259 N.s/m^2[SAE -50] given rightarrow parameter are mass of head m rightdoublearrow 0.8lbm rightdoublearrow 0.3628Kg diameter of cylinder = 0.5inches piston gead diameter rightdoublearrow 0.45 inches d = 0.01143 m C rightdoublearrow D - d rightdoublearrow = 0.05 inches newtons law of viscosity state that shear stress between adjacent fluid lauer is proportional to the velocity gradient between the two layer numerically it can be shown as rightarrow tau = nv/c rightdoublearrow F/A rightdoublearrow mg/A rightdoublearrow mg/Pi d l where n is dynamic viscosity of motor oil, c is clear cure V is velocity of piston head m is mass of piston head A is surface area of head mg/pi d rightdoublearrow = n_1 v_1/c 0.3628 times 9.8 /pi times 0.01143 times 1 rightdoublearrow 0.17 times v_1 /0.00127 v_1 rightdoublearrow 0.3628 times 9.8 times 0.00127/pi times 0.001143 times 0.17 v_1 = 0.74 ms^-1