Basics. Check the following statement correct or not, and explain why.

 

S1. A rigid body rotates about a fixed axis x, with the angular rotation rate, , the kinetic energy of the body is where is the moment of the inertia of the body about the axis, x.

 

S2. A wheel subject to an external force moves along a horizontal rough surface, the friction force from ground on the wheel is N . is the static friction coefficient between the wheel and rough surface, and N is the normal supporting force from ground surface to the wheel.

Assuming a linear velocity profile, find the boundary layer thickness the wall shear stress, the displacement thickness and the drag for a flat plate with zero pressure gradient and free stream velocity U0. The plate has length L and width b. Do you have flow separation? If the answer is yes or no, explain why.

3. Explain why, for a gas, the specific heat at constant volume has a different value 
from the specific heat at constant pressure.
An ideal gas is contained in a cylinder fitted with a piston. Initially the temperature of the 
gas is 15℃. If the mass of the gas is 0.035 kg, calculate the quantity of heat energy 
required to raise the temperature of the gas to 150 ℃ when:
(a) The piston is fixed;
(b) The piston moves and the pressure is constant.
For the gas, 𝑐𝑣 = 676 J/kg-K and 𝑐𝑝 = 925 J/kg-K.

We are drilling a hole at a depth of 4,000 ft with an 8 ½ in bit and a mud weight of 15 ppg, where the formation is abnormally pressurised. Formation pressure is 2400 psi, therefore a casing should be run at 4,500 ft to seal off this formation. There are Grade C-75 and N-80 casings available, C-75 Grade is 20.00 lb/ft (ID=6.456”, OD=7”) and N-80 is 17.00 lb/ft (ID= 6.538”, OD=7”). Analyse if both, neither or one of the casing Grades can withstand the formation pressure and will not collapse at the reported conditions. Use the API formulas and tables