I need the answer as soon as possible Time :-2 hour.v = y + 3yz what he general form of velocitycomponent w(x,y,z) that satisfies the continuity equation?Q (2):- Two of the three velocity comporknts for incompressible fiow areQ (1);-From see-level find the T,P,p,a.k at 16 km?Q (2):- Two of the three velocity components for incompressible flow areu = x - 3xzv= v3 + 3yz what he general form of velocity%3D%3Dcomponent w(x,y,z) that satisfies the Contnuity equation?Q (3):- Airfoil between two parallel plates as shou

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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 the steady, two-dimensional velocity field of : V-›= (u, ? ) = (0.5 + 0.8 x) i-›+ (1.5 − 0.8 y) j-› where lengths are in units of m, time in s, and velocities in m/s. There is a stagnation point at (−0.625, 1.875) as shown in Fig. Streamlines of the flow are also plotted in Fig. Calculate the various kinematic properties, namely, the rate of translation, rate of rotation, linear strain rate, shear strain rate, and volumetric strain rate. Verify that this flow is incompressible.
A two-dimensional incompressible velocity fi eld has u =K (1 - e - ay ), for x ≤ L and 0 ≤ y ≤ ∞. What is the mostgeneral form of υ ( x , y ) for which continuity is satisfi edand υ = υ 0 at y= 0? What are the proper dimensions forconstants K and a ?
Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 s
Given the steady, incompressible velocity distribution V =3 x i + Cy j + 0 k , where C is a constant, if conservation ofmass is satisfi ed, the value of C should be( a ) 3, ( b ) 3/2, ( c ) 0, ( d ) - 3/2, ( e ) - 3
The velocity field of a flow is described by V-›= (4x) i-›+ (5y + 3) j-›+ (3t2)k-›. What is the pathline of a particle at a location (1 m, 2 m, 4 m) at time t = 1 s?
3.3 Verify whether or not the following difference representation for the continuity equation for a 2-D steady incompressible flow has the conservation property: (u, 1.j + u;41.j-1 - u.; – 4j.j-1) (1,j – 41,j-1) 2 Ax Ay where u and v are the x and y components of velocity, respectively. 3.4 Repeat Prob. 3.3, for the following difference representation for the continuity equation: (4i+ 1,5 - Uj-1,) (u, j+1 - V,j-1) + 2 Ax 2 Ay
For a given hypothetical flow the velocity at time t = 0 to t = 10 s was u = 0, v = 4m/s. Then from time t = 10 s to t = 15 s, the velocity was u = - 2 m/s, v = 2 m/s. A dye streak was started at a point in the flow field at time t = 0, and the path of a particle in the fluid was also traced. Draw to scale the streakline, pathline of the particle and streamlines at t = 15 s.
This problem will show you how to obtain the pathline and the streamline for a velocity field. A velocity field is given by u=(ax_1 t)i −(bx_2)j , where a=0.1^s−2 and b=1s^−1. (a) For the particle that passes through the point (x1,x2) = (1,1) at instant t = 0, get the equation of the pathline during the interval from t = 0 to t = 3s. Plot it roughly by hand(b) Get the equations of the streamlines through the same point at the instants t = 0,1, and 2s. Plot it roughly by hand
3.3 Starting with a small fluid element of volume dx dy dz, derive the continuity equation (Eq. 3.4) in rectangular cartesian coordinates.
1. A Cartesian velocity field is defined by V = 2xi + 5yz2j − t3k. Find the divergence of the velocity field. Why is this an important quantity in fluid mechanics? 2. Is the flow field V = xi and ρ = x physically realizable? 3. For the flow field given in Cartesian coordinates by u = y2 , v = 2x, w = yt: (a) Is the flow one-, two-, or three-dimensional? (b) What is the x-component of the acceleration following a fluid particle? (c) What is the angle the streamline makes in the x-y plane at the point y = x = 1?
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. Prove that the flow field specified is not incompressible;i.e., it is a compressible flow as stated without proof .
For a flow in the xy plane, the x component of the velocity is u=3x2y-y3is given. Determine the y component for steady state and incompressible flow. Does this result also apply to unstable, incompressible flow? Why is that? How many possible y components are there? Discuss.

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component w(x,y,z) that satisfies the Continuity equation? u = x - 3xz Q (2):- Two of the three velocity compontnts for incompressible flow are v= y + 3yz watEhe general form of velocity %3D component w(x,y,z) that satisfies the ontinuity equation?