FM ENG1243/ENG60203 Tutorial 01-Q Semester 1503

Q1. Evaluate (80 MN/s)(5 mm)2, and express the result with SI units.

Q2. Air contained in a cylindrical tank of radius 1.5 m and length of 4 m under an absolute pressure of 60 kPa and temperature of 60℃. Determine the mass of the air in the tank.

Q3. If 1 cup of cream having density of 1005 kg/m3 is turned into 3 cups of whipped cream, determine the specific gravity and specific weight of the whipped cream.

Q4. Describe graphically the no-slip conditions for the following cases:

(a) An object moves on the horizontal surface covered by thin layer of Newtonian fluid.(b) Stationary plate between two plates separated by a thin layer of Newtonian fluid

moving in same direction.(c) Two plates separated by a thin layer of Newtonian viscous medium are moving in

opposite directions with same speed.(d) Water (Newtonian fluid) flows with speed v in a horizontal cylindrical pipe.

Q5. The pressure difference, ∆ p , across a partial blockage in an artery (called a stenosis) is approximated by the equation

∆ p=KμμvD

+Ku( A0

A1

−1)2

ρ v2

where v is the blood velocity, μ is the blood viscosity (FL-2T), ρ is the density (ML-3), D is the artery diameter, A0 is the area of unobstructed artery, and A1 is the area of the stenosis.

Determine the dimensions of the constants K μ and Ku. Would this equation be valid in any system of units?

Q6. If F is a force and x is a length, what are the dimensions in FLT system of (a) dFdx, (b)

d3Fd x3 ,

(c) ∫F dx?

Q7. A block of weight W slides down an inclined plane on a thin film of oil, as in the figure. The film contact area is A and its thickness h. Assuming linear velocity distribution in the film, derive an analytic expression for the terminal velocity v of the block.

Q8. The belt in the figure moves at steady velocity v and skims the top of a tank of oil of viscosity μ. Assume a linear velocity profile, develop a simple formula for the belt-drive power P required as a function of h , L , v, and μ .