I need it ASAP and correctly Show by dimensional analysis that this leads to the logarithmic overlap relation (6.28).The following turbulent flow velocity data u(y), for air at24°C and 1 atm near a smooth flat wall were taken in theUniversity of Rhode Island wind tunnel:Y, mm0.640.891.191.401.65и, m/s15.616.517.317.618.0Estimate (a) the wall shear stress and (b) the velocity u aty = 5.6 mm.

Given DataT=24°Cair Density and kinematic viscosity at 24°C from dataρ=1.225kg/m3ϑ=1.543m2/s

Answered: Show by dimensional analysis that this…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Consider a rectangular wing mounted in a wind tunnel. The wing model completely spans the testsection so that the flow sees essentially an infinite wing. The wing has a NACA 2421 airfoil section,a chord of 3.0 m, and a span of 20 m. The tunnel is operated at the following test conditions: P =101,000 N/m2; T = 35° C; V = 50 m/s; and µ = 1.9 * 10 -5 kg/(m s).(a) Determine the operating Reynolds number.(b) Calculate the lift, drag, and moment about the aerodynamic center for an angle of attack of 8 deg andRe=9*106(c) At a Reynolds number of 3 * 106, find the following:1) What is the stalling angle of attack for this airfoil?2) What is the angle of attack for zero lift?3) What is the lift-curve slope?
Select an appropriate set of variables that influencethe drag force FD on an airfoil (Fig. P6.23) andwrite the final form in terms of dimensionlessparameters.
A sample of powdered zinc oxide, density 5.60g/cm 3 , is allowed to settle under the accelerationof gravity, 981 cm/sec 2 , at 25 25°C. The rate ofsettling, v, is 7.30 ×10 3 cm/sec; the density ofthe medium is 1.01 g/cm 3 , and its viscosity is 1centipoise = 0.01 poise or 0.01 g/cm sec.Calculate the Stokes diameter of the zinc oxidepowder.Problem:
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.
SAE 30 oil at 20 °C flows at 1.8 ft3/s from a reservoir into a6-in-diameter pipe. Use flat-plate theory to estimate theposition x where the pipe wall boundary layers meet in thecenter. Compare with Eq., Le/d≈ 0.06 Red laminar and give some explanationsfor the discrepancy.
Q.10. To predict the drag on an aircraft at a flight speed of 150 m/s, where the condition of air is such that the local speed of sound is 310 m/s, a pressurized low temperature tunnel is used. Density, viscosity and local sonic velocity at tunnel condition are 7.5 kg/m³, 1.22 x 10-5 Ns/m² and 290 m/s. Determine the flow velocity and the scale of the model. Assume full dynamic similarity should be maintained. Density and viscosity at the operating conditions are 1.2 kg/m³ and 1.8 x 10 Ns/m².
Aerodynamics NACA 747A415, chord is 180 cm 1) What is the location of favorable pressure gradient of the upper surface, measured from LE? 2) What is the location favorable pressure gradient of the upper surface, measured from TE?
Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Consider the nonlifting flow over a circular cylinder of a given radius,where V∞ = 20 ft/s. If V∞ is doubled, that is, V∞ = 40 ft/s, does theshape of the streamlines change? Explain.
A small, axisymmetric, low-speed wind tunnel is built to calibrate hot wires. The diameter of the test section is 6.68 in, and its length is 12.5 in. The air is at 60°F. At a uniform air speed of 5.0 ft/s at the test section inlet, by how much will the centerline air speed accelerate by the end of the test section? What should the engineers do to eliminate this acceleration?
When fluid in a long pipe starts up from rest at a uniformacceleration a , the initial flow is laminar. The flow undergoesa transition to turbulence at a time t * which depends, tofirst approximation, only upon a , ρ , and μ . Experiments by P. J. Lefebvre, on water at 20 8 C starting from rest with 1-gacceleration in a 3-cm-diameter pipe, showed transition att * = 1.02 s. Use this data to estimate ( a ) the transition timeand ( b ) the transition Reynolds number Re D for water flowaccelerating at 35 m/s 2 in a 5-cm-diameter pipe.
Consider steady flow of air through the diffuser portion of a wind tunnel. Along the centerline of the diffuser, the air speed decreases from uentrance to uexit as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.
A smooth wooden sphere (SG = 0.65) is connected by athin rigid rod to a hinge in a wind tunnel, as in Fig. Air at 20°C and 1 atm flows and levitates the sphere.(a) Plot the angle θ versus sphere diameter d in the range1 cm≤ d≤15 cm. (b) Comment on the feasibility of thisconfiguration. Neglect rod drag.

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