Calculate the pressure of the air in the sealed tank shown in Fig. 6.25 that would cause the velocity of flow to be 20 ft/s from the nozzle. The depth his 10 ft.
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Calculate the pressure of the air in the sealed tank shown in Fig. 6.25 that would cause the velocity of flow to be 20 ft/s from the nozzle. The depth his 10 ft.
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- Under laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?Theodore von Kármán in 1930 theorized that turbulentshear could be represented by τturb = ε du/dy, whereε= ρκ2y2|du/dy| is called the mixing-length eddy viscosityand κ ≈ 0.41 is Kármán’s dimensionless mixing-lengthconstant [2, 3]. Assuming that τturb ≈ τw near the wall,show that this expression can be integrated to yield thelogarithmic overlap la).A mixed berries cordial manufacturer changed to 5 m stainless steel tubing due to highamount of energy drop recorded in the previous material. Calculate the pressure drop permeter length for the cordial if relative roughness, velocity, density, viscosity, and friction inthe pipe are given as 0.0015, 1.5 m/s, 1120 kg/m3,1.6 X10-3 kg/m s and 0.07, respectively.
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- An engineer monitored a flow of gasoline of about 50 m3/h and of density ,ρ 680 kg/m3 through a 10-cm-diameter smooth pipe. If the engineer used an orifice plate of a long-radius flow through the nozzle, or a venturi nozzle, all with 5-cm-diameter throat. The differential pressure gauge available was accurate in the range 30 to 60 KPa and of dynamic viscosity, μ 2.92E-4 kg/m-s. Without considering flow losses, which device is best?We are given laboratory data, taken by Prof. Robert Kirchhoffand his students at the University of Massachusetts, for thespin rate of a 2-cup anemometer. The anemometer wasmade of ping-pong balls ( d = 1.5 in) split in half, facing inopposite directions, and glued to thin ( 1/4-in) rods pegged toa center axle. There were fourrods, of lengths l = 0.212, 0.322, 0.458, and 0.574 ft. Theexperimental data, for wind tunnel velocity U and rotationrate Ω , are as follows: Assume that the angular velocity Ω of the device is afunction of wind speed U , air density ρ and viscosity μ , rodlength l , and cup diameter d . For all data, assume air is at1 atm and 20 ° C. Defi ne appropriate pi groups for thisthe problem, and plot the data in this dimensionless manner.Comment on the possible uncertainty of the results.As a design application, suppose we are to use thisanemometer geometry for a large-scale ( d = 30 cm) airportwind anemometer. If wind speeds vary up to 25 m/s and wedesire an average…Apply the necessary conversion factors to prove the relationship between dimensionless turbine specific speed and customary U.S. turbine specific speed, NSt = 43.46NSt, US. Note that we assume water as the fluid and standard earth gravity.
- In the flow of air at 20°C and 1 atm past a flat plate inFig. , the wall shear is to be determined at position x bya floating element (a small area connected to a strain-gageforce measurement). At x = 2 m, the element indicates ashear stress of 2.1 Pa. Assuming turbulent flow from the leadingedge, estimate (a) the stream velocity U, (b) the boundarylayer thickness δ at the element, and (c) the boundary layervelocity u, in m/s, at 5 mm above the element.An important parameter in certain types of fluidflow problems when a free surface is present is the Froudenumber (Fr), which can be expressed in equation form.where p is the density of the fluid, v is a velocity, L is alength, and w is the specific weight of the fluid. Show thatthe Froude number is dimensionless.Air at 20°C and 1 atm enters a 40-cm-square duct as in Fig.P7.7. Using the “displacement thickness” concept estimate (a) the mean velocity and (b) the mean pressure inthe core of the flow at the position x = 3 m. (c) What is theaverage gradient, in Pa/m, in this section?