Using the basic principle of Navier-Stokes equations, derive the expressions for volume flow rate, average velocity and velocity distribution profile for a steady laminar flow in a circular tube. How these expressions can be modified for similar flow in an annulus.
hydraulic system operates with a viscous fluid (dynamic viscosity 0.02 kg/m.s, specific gravity 0.9) at gauge pressure of 22MPa and . The control valve consists of a piston 20mm long with 25mm diameter, fitted to a cylinder with mean radial clearance of 0.005mm. Determine the leakage flow rate if the gauge pressure on the low-pressure side of the piston is 1 MPa.
The crankshaft journal bearing in an automobile engine is lubricated by SAE30 oil (dynamic viscosity 0.02 kg/m.s, specific gravity 0.9) at . The bearing has the length of 4cm and diameter of 8cm. The crankshaft rotates at 3000rpm and the diametric clearance between the shaft and the bearing is 1mm. Calculate the power required to overcome friction when there is no load on the bearing.
A liquid having dynamic viscosity of 0.02 kg/m.s, specific gravity 0.9 flows between two horizontal plates 25mm apart. If the average velocity is 0.3m/s, estimate the shear stress at the wall, 5mm and 10mm vertically from the wall. Plot the velocity and shear stress distributions over the channel depth.
rectangular plate of face area is drawn over a horizontal layer of fluid 5mm thick and supported by a solid plate at rest. The force required to draw the upper plate at a steady speed of 0.6m/s is 25N. Estimate the value of viscosity of the fluid and also plot the velocity profile.
. The control valve consists of a piston 20mm long with 25mm diameter, fitted to a cylinder with mean radial clearance of 0.005mm. Determine the leakage flow rate if the gauge pressure on the low-pressure side of the piston is 1 MPa.
. The bearing has the length of 4cm and diameter of 8cm. The crankshaft rotates at 3000rpm and the diametric clearance between the shaft and the bearing is 1mm. Calculate the power required to overcome friction when there is no load on the bearing. 
face area is drawn over a horizontal layer of fluid 5mm thick and supported by a solid plate at rest. The force required to draw the upper plate at a steady speed of 0.6m/s is 25N. Estimate the value of viscosity of the fluid and also plot the velocity profile.