presentation problems.docx

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 w. 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 2 A 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 m 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 δ 1 = 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 10 3 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 viscosity= 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 5 The 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/m 3 and the dynamic viscosity is 1 cP. Determine the flow region (Stokes' law, transition or Newton's law regions) where the spheres are moving.