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mt2-solutions

mt2-solutions - ME331 Midterm 2 Spring 2009 18.4.2009...

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Unformatted text preview: ME331 Midterm 2 Spring 2009 18.4.2009 10:00-12:00 Closed Book Name: 1. Water is discharged from a 1cm diameter nozzle and it strikes a curved vane as shown. Determine the force that the water jet exerts on the vane. Neglect the weight of water and all viscous effects. K 1. vane “9451’“ _ lom'ﬁz. _ Q4. .. lanai-511°; 'Pa'?°.\‘"‘_g% m v“ 4- v _ \I -_-_ ?_W- 513% ‘ Mr”, 1:52.170 4 a. Q ~ 7. q- - ,0 V4. ~1— A JLAL G \jA A — z. av‘l: 15‘ _15V¢. llooo?“ =- 690 m3 .4: 41 vVM-dA =Fm’6 cosgo'Vm'D =F>4 ® 3 d1- V1.- ‘1' Vt‘ﬂ/‘L +3 -AN ”3 9. I" X 1’ T; 5111'. ‘4’ z X 2; v:.Tlp%-}( 30 3 ME331 Midterm 2 Spring 2009 18.4.2009 10:00—12:00 Closed Book Name: 1‘ 4 2. An oil film (of thickness 6=3mm and width w=1m} is flowing steadily on an inclined plane. ‘ Flow is fully developed. Viscosity of the oil is 0.03 Ns/mZ and the density is 800 kg/ma. Determine the volumetric flow rate and the shear stress on the wall, if the inclinatidn angle is ME331 Midterm 2 Spring 2009 18.4.2009 10:00-12:00 Closed Book Name: 3. The drag force acting on a race car is to be determined experimentally. The important parameters which effect the drag force FD are fluid properties, such as p, p, c, kinematic properties, such as u, and geometric properties, such as L, D. {6 a. Use dimensional analysis to determine the functional relationship, which describes this flow. to b. The original race car has L=3m, D=1m and moves at a speed of 600 km/h in air (p=1,225 kg/m3, i.L=1,8-10‘6 Pa.s, c=340 m/s). The experiments are to be performed with water instead of air (p=1000 kg/m3, p=10'3 Pa.s, c=1500 m/s). What should the L, D and u values be, in order to achieve a similar test setup. a) alsmwiwhb 4mm “.th w Rare“? ”“9““ 5,4,1). li WW: FD .- 91,: 7’?" ’ Cb /§VL 2. l... ﬁzz?! an CD;((MQI&/ E) [4,!“ = 035.3 m/s 500 _ _._,. Mm L.” 600 NIE331 Midterm 2 Spring 2009 13.4.2009 10:00-12:00 Closed Book Name: 4. Waterflows into a cylindrical pipe with circular cross—section (radius R, length L) with uniform velocity proﬁle. Under steady ﬂow conditions, boundary layer developes along the flow direction and finally a fully developed velocity profile occurs for the laminar flow. , v _ uuuuu r’ uniform :1“ i\$i velocity -—«-~ proﬁle H parabolic .. velocity proﬁle ntrance reg'o Fully developed ﬂow Boun-ary layer a. Determine the velocity profile, i.e. u(r) at the exit. b. Determine the total shear force Fsh acting on the pipe surface, if the pressure drop between the inlet and outlet is AP. c. Write the extended Bernoulli equation for this flow between the inlet and outlet. Determine the hlvalue for this flow. I) {2M 244-2: :9. @l “*3 “to“ 1—}: vibe?” ‘5 ‘4‘ 9M ﬂ 4 {ktic a“ 3(3)» 3% State (a) Fm L23 ...
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