Make and state any assumption you consider necessaryDerive the boundary layer equations for 2D turbulent flow.Hint: Start with the full governing equations for turbulent flow when the mean motion istwo-dimensional.дӣ+ддх ду=(2.95)дӣдӣ-(u²)1+0=12+1 (213) - [+]Ӣдх дудхд+ Vду=-р дхдрдейдей+vдх2 дугдейдей1 дрр дуk+v+-(u'v') +( - +3дх² дуг+of+1 of = (+) (#²²+3)-[2+27]отидх-=отдутдх² дуг(2.106)·(u'T') (v'T'(2.115)дх

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Answered: Make and state any assumption you…

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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The slope of the height h of a surface wave moving in a shallow pool of liquid is related to the speed of the wave u and gravity g by the following equation и ди дх g əx (a) Use a length scale L and a velocity scale Vo to 'nondimensionalize' the equation (b) What is the nondimensional parameter of the flow?
PLS SHOW ME FULL STEPS SIR PLS ANSWER WITHIN 30 MIN SIR SUBJECT (FLUID MECH 2) use setting 2
The Reynolds transport theorem (RTT) is discussed in Chap. 4 of your textbook. For the general case of a moving and/or deforming control volume, we write the RTT as follows: d pb dV + pbV-ñ dA dt dt dB sys where Vr is the relative velocity, i.e., the velocity of the fluid relative to the control surface. Write the primary dimensions of each additive term in the equation and verify that the equation is dimensionally homogeneous. Show all your work. (Hint: Since B can be any property of the flow-scalar, vector, or even tensor—it can have a variety of dimensions. So, just let the dimensions of B be those of B itself, {B}. Also, b is defined as B per unit mass.)
M1
A small low-speed wind tunnel is designed to calibrate hot wires (anemometer wires) (Figure 2). The air temperature is 19 OC. The test section of the wind tunnel is 30 cm in diameter and 30 cm in height. The flow through the test section must be as uniform as possible. The speed range of the wind tunnel varies from 1 M/s to 8 M/S, and the design will be optimized with an airspeed of V= 4.0 M / s in the test section. For a flow state at a speed of 4.0 m/S, which is almost uniform at the entrance to the test section, how fast does the air velocity on the tunnel axis accelerate to the end of the test section?Note: kinematic viscosity of air at 19 C ν=1. 507x10-5 m2 / s
How do you get from equation 3.1.1 to 3.1.5? I understand that yoy mutiply both sides by Ui, but I'm confused on the math that is done to bring Ui into the partial derivative. Please show all intermediate steps.
i need the answer quickly
The one-dimensional motion experiment carried out in the air table experimental setup. the results are indicated in the table below. (1.jpg) a) Calculate the theoretical speed value belonging to the motion. b) Calculate the experimental velocity value by drawing the graph with the table values above. c) Calculate the percentage error by comparing the obtained theoretical and experimental values.
The wind flutter on the wing of a newly proposed jet fighter is given by the following 1st order differential equation: dy/dx = 2yx With the Boundary Condition: y(0) = 1 (remember this means that y = 1 when x = 0) Determine the vertical motion (y) in terms of the span (x) of the wing. The frequency of fluctuations of the wing at mach 2 is given by the non-homogenous 2nd order differential equation: y'' + 3y' - 10y = 100x With the boundary conditions: y(0) = 1 and y(1) = 0 (i.e., y = 1 when x = 0 and y = 0 when x = 1) By solving the homogenous form of this equation, complete the analysis and determine the amplitude (y) of vibration of the wing tip at mach 2. Critically evaluate wing flutter and fluctuation frequency amplitude determined by solving the two differential equations above.
provide explanation and free body diagram for each part also comment
[1] 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 ut 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, Dee x=0 to x=L.
In the field of air pollution control, one often needs to sample the quality of a moving airstream. In such measurements a sampling probe is aligned with the flow as sketched in Fig. A suction pump draws air through the probe at volume flow rate V· as sketched. For accurate sampling, the air speed through the probe should be the same as that of the airstream (isokinetic sampling). However, if the applied suction is too large, as sketched in Fig, the air speed through the probe is greater than that of the airstream (super iso kinetic sampling). For simplicity consider a two-dimensional case in which the sampling probe height is h = 4.58 mm and its width is W = 39.5 mm. The values of the stream function corresponding to the lower and upper dividing streamlines are ?l = 0.093 m2/s and ?u = 0.150 m2/s, respectively. Calculate the volume flow rate through the probe (in units of m3/s) and the average speed of the air sucked through the probe.

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