No 1. Group 1 Air flows in a horizontal plate of sides 200 mm long x 100 mm wide. At a section a few meters from the entrance, the turbulent boundary layer is of thickness δ1= 5.25 mm, and the velocity in the inviscid central core is U1= 12.5 m/s. Farther downstream the boundary layer is of thickness δ2= 24 mm. The velocity profile in the boundary layer is approximated well by the 1/7-power expression. Find the velocity, U2, in the inviscid central core at the second section, and the pressure drop between the two sections. Density of air =1.23 kg/m3 and kinematic viscosity = 1.5x10-5 m2/sec.

No 2. Group 1 A viscous solution containing particles of density p= 1461 kg/m3 and of various sizes is to be clarified by centrifugation. The solution density = 801 kg/m3, and its viscosity is 100 cp. The centrifuge has a bowl with r2 = 0.02225 m, r1 =0.00716 m, and height b = 0.1970 m. Calculate the smallest diameter of particles which reach the bowl wall if N = 23,000 rev/min and the flow rate q = 0.002832 m3/h. The residence time tr is equal to the volume of liquid V m3 in the bowl divided by the feed volumetric flow rate q in m3/s. The volume V = b(r2- r1). Assume Stokes' law applies.

No 3. Group 2 Consider two-dimensional laminar boundary-layer flow along a flat plate. Assume the velocity profile in the boundary layer is sinusoidal, u/U = sin (/2 y/δ) where U is a constant.Find:a. The boundary layer thickness, δ, as a function of x. Use momentum integral equation

involving tw.b. The displacement thickness, δ*, as a function of x.c. The total friction force on a plate of length L and width b as a function of ReL.

No 4. Group 2A cyclone separator is used to remove sand grains from an airstream at 150°C. If the cyclone body is 0.6 m in diameter and the average tangential velocity near the wall is 16 m/s, what are rates of rotation in revolution/sec and in radian/sec, what is centrifugal acceleration (r.2) near the wall and what is the terminal velocity near the wall of particles of 20 and 40 mm diameters respectively? Check with Galileo number to obtain correct region range of R'/(u2). How much greater are the terminal velocity in centrifugal settling compared to that in gravity settling? Density of grains = 2196 kg/m3.

No 5. Group 3

A laboratory wind tunnel has a test section that is square in cross section at section 1, with inlet width W1 and height H1, each equal to 305mm. At freestream speed U1 = 24.4 m/s, measurements show the boundary-layer thickness is δ1 = 10mm with a 1/7-power turbulent velocity profile. The pressure gradient in this region is given approximately by dp/dx = -0.035 mm H2O/mm. a. Evaluate the reduction in effective flow area caused by the boundary layers on the tunnel

bottom, top, and walls at section 1 .b. Calculate the rate of change of boundary-layer momentum thickness, dθ/dx, at section 1. c. Estimate the momentum thickness at the end of the test section, located at L = 2540 mm

downstream.

No 6. Group 3. A particle of 1 mm diameter and density 1.1 x 103 kg/m3 is falling freely in an oil of 900 kg/m3 density and 0.003 Nsm-2 viscosity. Assuming that Stokes' law applies, how long will the particle take to reach 99% of its terminal velocity? What is the Reynolds number corresponding to this velocity?

No 7. Group 4 (cubic law)The velocity distribution inside a laminar boundary layer over a flat plate is described by the cubic law:u/U = a0 + a1(y/) + a2(y/)2 + a3(y/)3. At y=0, 2u/y2 = 0. What is velocity profile in the boundary layer after determining values of all constants? What is relationship between and ?. Determine correlation between and Rex

No 8. Group 4 A mixture of silica (B) and galena (A) solid particles having a diameter range of 5.21 x 10-6 m to 2.50 x 10-5 m is to be separated by hydraulic classification using free settling conditions in water at 293.2 K at some water velocities to get 3 fractions of material (pure galena, mixed galena-silica, pure silica). The density of silica is 2650kg/m3and that of galena is 7500 kg/m3. The water viscositym= 1.005 x 10-3 Pa.s = 1.005 x 10-3 kg/(m.s) and its density = 998 kg/m3. Calculate the diameter ranges of the 3 fractions obtained in the settling and corresponding 2 terminal velocities. If the settling is in the laminar region, the drag coefficients will be reasonably close to that for spheres. Assume Stokes' law applies.

No 9. Group 5The velocity distribution inside a laminar boundary layer over a flat plate is described by the fourth order polynomial:u/U = a0 + a1(y/) + a2(y/)2 + a3(y/)3+ a4(y/)4. At y=0, 2u/y2 = 0 and y=, 2u/y2 = 0. What is velocity profile in the boundary layer after determining values of all constants? What is relationship between and ?. Determine correlation between and Rex

No 10. Group 5 Small glass spheres are suspended in an upwards flow of water moving with a mean terminal velocity of 0.05 m/s. Calculate the diameter of the spheres. The density of glass is 2630 kg/m3. The density of water is 1000 kg/m3 and the dynamic viscosity is 1 cP. Determine the flow region (Stokes' law, transition or Newton's law regions) where the spheres are moving.