Chapter 5, Problem 5.31P

A large plate is pulled at a constant speed of U = 4 m/s over a fixed plate on 5-mm-thick engine oil film at 20°C. Assuming a half-parabolic velocity profile in the oil film, as sketched, determine the shear stress developed on the upper plate and its direction. What would happen if a linear velocity profile were assumed?

2.  What is the difference between laminar and turbulent flow, and how does this affect fluid mechanics in mechanical engineering?

An 16-kg slab slides down a 25° inclined plane on a 4-mmthick film of SAE 30 oil at 15.6 °C; the contact area is0.3m2. Find the terminal velocity of the slab.  Explain ur answer

Can you explain the fundamental principles of fluid dynamics and their practical applications in mechanical engineering? Specifically, delve into concepts such as Bernoulli's principle, Reynolds number, and the Navier-Stokes equations, and elaborate on how these principles are utilized in designing and optimizing various systems, such as aircraft aerodynamics, turbine engines, and piping networks for fluid transport?

A sea-level automobile tire is initially at 32 lbf/in2 gagepressure and 75 °F. When it is punctured with a hole that resemblesa converging nozzle, its pressure drops to 15 lbf/in2gage in 12 min. Estimate the size of the hole, in thousandthsof an inch. The tire volume is 2.5 ft2.

A square block weighing 1.1 kN and 250 mm on an edge slides down an incline on a film of oil 6 micrometer thick. Assuming a linear velocity profile in the oil and neglecting air resistance, what is the terminal velocity of the block in m/s? The viscosity of oil is 7mPa-s and the angle of inclination is 20deg.

A 0.75 m by3m flat plate is towed at 5 m/s on a 2.5-mm-thick layer of SAE-30 oil at 38°C, with absolute viscocity of 100 cP,that separates it from a flat surface. The velocity distribution between the plate and the surface is assumed to be linear. What force is required if the plate and surface are horizontal?

Fluid from a large reservoir at temperature T 0 fl ows into acircular pipe of radius R . The pipe walls are wound with anelectric resistance coil that delivers heat to the fl uid at a rateq w (energy per unit wall area). If we wish to analyze thisproblem by using the full continuity, Navier-Stokes, andenergy equations, what are the proper boundary conditionsfor the analysis?

An expression for the laminar velocity profile on a flat plate is u=C1sin(C2y)+C3 Where the argument of the sine function is in radians. Using the three common physicalconditions that the velocity profile should satisfy, determine  a) the constants C1, C2, and C3.b) the nondimensional velocity profilec) the boundary thickness (δ/x) as a function of lengthd) the skin friction coefficient, Cf as a function of lengthe) displacement thickness (δ*/x) as a function of lengthf) the momentum thickness (θ/x) as a function of lengthg) the drag force (FD) on both sides of the plate