b) A wind stress of 0.2 N m-2 blows along a narrow (no Coriolis force acting) freshwater channel 10 m deep and that is open ended and the water is initially stationary. After a time of 2000s, the current in the channel reaches a steady value throughout the channel and is then balanced only by the vertical component of the turbulent friction. Estimate; (i) the average current reached in the channel after a time of t=2000 s (ii) A value of Az, the vertical turbulent eddy viscosity coefficient

b) A wind stress of 0.2 N m-2 blows along a narrow (no Coriolis force acting) freshwater channel 10 m deep and that is open ended and the water is initially stationary. After a time of 2000s, the current in the channel reaches a steady value throughout the channel and is then balanced only by the vertical component of the turbulent friction. Estimate; (i) the average current reached in the channel after a time of t=2000 s (ii) A value of Az, the vertical turbulent eddy viscosity coefficient

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.29P: Air at 20C flows at 1 m/s between two parallel flat plates spaced 5 cm apart. Estimate the distance...

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Air at 20C flows at 1 m/s between two parallel flat plates spaced 5 cm apart. Estimate the distance from the entrance to the point at which the hydrodynamic boundary layers meet.
A wind stress of 0.2 N m-2 blows over an initially stationary freshwater lake, 20 km long, and moves water downwind in the upper 10 m of the 20 m deep lake. (a) Estimate the difference in lake level between the ends of the lake in the direction of the wind one would expect when the wind force is balanced by the opposing pressure force in the upper 10 m (assuming no Coriolis influence in the dynamical balance) (b) The current driven in the lower 10 m by the pressure force which is balanced by the vertical frictional forces characterized by a coefficient of vertical turbulent eddy viscosity Az=0.02 m2 s -1 .
Water at 20 ° C fl ows through the elbow in Fig. P3.60 andexits to the atmosphere. The pipe diameter is D 1 = 10 cm,while D 2 = 3 cm. At a weight fl ow rate of 150 N/s, thepressure p 1 = 2.3 atm (gage). Neglecting the weight ofwater and elbow, estimate the force on the fl ange bolts atsection 1.
A settling tank for municipal water supply is 2.5 m deep,and 20°C water fl ows through continuously at 35 cm/s.Estimate the minimum length of the tank that will ensurethat all sediment (SG = 2.55) will fall to the bottom forparticle diameters greater than (a) 1 mm and (b) 100 μm.
A 98% efficient ESP is to treat a gas stream flowing at 5000 m3/ min. If the effective drift velocity is 6.0 cm/s, calculate the number of plates if each plate is 6 m hy 10 m, and there are 3 mechanical fields.
Water exits a 1-cm diameter outlet of a faucet. Estimate the maximum speed that would result in a laminar flow if the water temperature is 50°C. Assume Re = 2000 a. 558 m b 6.15 m c7.71 m d 845 m
Water at 20 ° C is delivered from one reservoir to anotherthrough a long 8-cm-diameter pipe. The lower reservoirhas a surface elevation z 2 =80 m. The friction loss in thepipe is correlated by the formula h loss ≈17.5( V 2 /2 g ), whereV is the average velocity in the pipe. If the steady fl ow ratethrough the pipe is 500 gallons per minute, estimate thesurface elevation of the higher reservoir.
By analogy with laminar shear, τ = μ du/dy, T. V.Boussinesq in 1877 postulated that turbulent shear couldalso be related to the mean velocity gradient τturb = ε du/dy,where ε is called the eddy viscosity and is much larger thanμ. If the logarithmic overlap law, is valid withτturb ≈τw, show that ε ≈ κρu*y.
Consider a flow of SAE 30W oil through a 3-cm-diameter pipe. For SAE 30W oil, take ρ = 891kg/m3, μ = 0.29 kg/m⋅s at 20 °C, and μ = 0.01 kg/m-s at 100 °C, and π = 22/7. For what flow rate in m3/h would a transition to turbulence take place at 20°C? The flow rate is m3/h.
A freshwater boat of mass 400 kg is supported by a rectangularhydrofoil of aspect ratio 8, 2 percent camber, and12 percent thickness. If the boat travels at 7 m/s and α = 2.5°,estimate (a) the chord length, (b) the power required ifCD∞ = 0.01, and (c) the top speed if the boat is refitted withan engine that delivers 20 hp to the water.
In this era of expensive fossil fuels, many alternativeshave been pursued. One idea from SkySails, Inc., shownin Fig. is the assisted propulsion of a ship by a largetethered kite. The tow force of the kite assists the ship’spropeller and is said to reduce annual fuel consumptionby 10–35 percent. For a typical example, let the ship be120 m long, with a wetted area of 2800 m2. The kite areais 330 m2 and has a force coefficient of 0.8. The kite cablemakes an angle of 258 with the horizontal. Let Vwind =30 mi/h. Neglect ship wave drag. Estimate the ship speed(a) due to the kite only and (b) if the propeller delivers1250 hp to the water. [Hint: The kite sees the relativevelocity of the wind.]
Given a turbulent diffusivity of 10 m2/s in the atmosphere, and a wind velocity of 1 m/s, can you estimate the size of a typical turbulent eddy when it is driven by mechanical mixing from the ground?