Homework 5 Problems (1)

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Georgia Institute Of Technology *

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3340

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Mechanical Engineering

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Apr 3, 2024

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Homework 5 Problems Problem 5.1.15 In the vortex tube shown in Fig. P5.1.15, air enters at 202kPa absolute and 300 K. Hot air leaves at 150 kPa absolute and 350 K, whereas cold air leaves at 101 kPa absolute and 250 K. The hot air mass flowrate, 71, equals the cold air mass flowrate, 77.. Find the ratio of the hot air exit area to cold air exit area for equal exit velocities. — - - e = Te = 250 K Ty=350K pc = 101 kPa py = 150 kPa e "H T = 300 K p = 202 kPa Figure P5.1.15 Problem 5.1.19 Two rivers merge to form a larger river as shown in Fig. P5.1.19. At a location downstream from the junction (before the two streams completely merge), the nonuniform velocity profile is as shown and the depth is 6ft. Determine the value of V. 08V 3 ft/s T Depth = 3 ft Figure P5.1.19

Problem 5.1.25 Flow of a viscous fluid over a flat plate surface results in the development of a region of reduced velocity adjacent to the wetted surface as depicted in Fig. P5.1.25. This region of reduced flow is called a boundary layer. At the leading edge of the plate, the velocity profile may be considered uniformly distributed with a value U. All along the outer edge of the boundary layer, the fluid velocity component parallel to the plate surface is also U. If the x- direction velocity profile at section (2) is u _i[z)_l(zj U 2\0) 2\0 develop an expression for the volume flowrate through the edge of the boundary layer from the leading edge to a location downstream at x where the boundary layer thickness is §. Section (2) Section (1) \ U Oute(r)fedge s =~~~ boundary ,,,, ‘f layer /’ 6 > | A Figure P5.1.25 Problem 5.1.30 A hypodermic syringe (see Fig. P5.1.30) is used to apply a vaccine. If the plunger is moved forward at the steady rate of 20 mm/s and if vaccine leaks past the plunger at 0.1 of the volume flowrate out the needle opening, calculate the average velocity of the needle exit flow. The inside diameters of the syringe and the needle are 20 mm and 0.7 mm. ) Oleak € o —>[ ) o Figure P5.1.30

Problem 5.2.16 A vertical jet of water leaves a nozzle at a speed of 10 m/s and a diameter of 20 mm. It suspends a plate having a mass of 1.5 kg as indicated in Fig. P5.2.16. What is the vertical distance h? Nl 5| L Figure P5.2.16 Problem 5.2.22 The plate shown in Fig. P5.2.22 is 0.5 m wide perpendicular to the paper. Calculate the velocity of the water jet required to hold the plate upright. d=10.0cm l ) e |/ Y T ) 20°C water jet H=0.5m 20°C water Pivot Figure P5.2.22

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Problem 5.2.34 In a turbulent pipe flow that is fully developed, the axial velocity profile is, o] as 1s illustrated in Fig. P5.2.34. Compare the axial direction momentum flowrate calculated with the average velocity, u, with the axial direction momentum flowrate calculated with the nonuniform velocity distribution taken into account. N 7\ \ / 7 = Rl\ "’I— u _{ — i.\ I_%‘ / \ Z A\l Figure P5.2.34