Consider the unsteady flow u= u0, v = kt, w = 0 where uo and k are positive constants. Show that the streamlines are straight lines, and sketch them at two different times. Also show that any fluid particle flows a parabolic path as time proceeds.

Q: When body is an equilibrium ,the net force is vanish

A: We have to check whether the given statement, "When body is an equilibrium, the net force is vanish"…

Q: Let R(t) = et+e be a particle position moving in the plane Then the acceleration at time zero is

A: We have the position vector given in terms of time t.                  Rt=et i+e-t j To find the…

Q: Given the space curve r(t) = (t, 2e", e²²), find the tangential and normal components of…

A: The tangential component of acceleration can be found by using the formula r'(t).r''(t)r'(t) The…

Q: 2. Find the r-component of the acceleration for the velocity field of a flow given by v(r, y, z,t) =…

A: NOTE: Hi! Thank you for the question. As per the honor code, we'll answer any one question in case…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x? + 3y² and the plane.x…

A:

Q: Let R(t) = e'i+ ej be a particle position moving in the plane. Then the acceleration at time zero is

A: Given, The position of moving particle is R(t)=et i+e-t j.

Q: The velocity components for a two dimensional fluid system can be given in the Eulerian system by u…

A: Given, u = 2x+2y+3t                             ...........1            v = x+y+12t…

Q: Determine the acceleration (vector and magnitude) of the fluid particle occupying the point (-2, 1,…

A: Accleration is given by  a→ =DV→Dt= ∂V→∂t+(V.→∇)V→Here, V→ =2xy i^+xz j^+yz k^Hence, ∂V→∂t= ∂2xy…

Q: When body is an equilibrium ,the net force is not vanish

A: False. The given statement is false. We know that: There are two conditions that must be met for an…

Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

A:

Q: Find the time required by the particle in passing between points which are at distances 4 and 2…

A:

Q: Find the positively oriented simple closed curve C for which the value of the line integral C(y^3…

A:

Q: Express the velocity and the acceleration of a moving point p(r,0)

A: We have given a curve in polar coordinate : r=1+sin(θ) with θ=t2…

Q: The velocity field for a fluid is given by V=(X2t3)i+(2XYT)j. The convective acceleration in the…

A: Given, V=x2t3i^+2xytj^ Here, u=x2t3 and v=2xyt Convective acceleration in y-direction is given by:…

Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: A slender rod of constant density lies along the line segment r(t) = tj + (2 - 2t)k, 0≤ t ≤ 1, in…

A:

Q: Compute the flux of water through parabolic cylinder S: y = x', from 0 < x < 2, 0 < z< 4 if the…

A:

Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

A:

Q: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…

A:

Q: 4) Find the equation of the tangent plane to the surface r(u, v) = (u²-v²)i − (3uv)j + (4√u+v)k when…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Let g(x,y,z)=5xe^y+yz^2. Use the gradient vector to find the equation of the tangent plane to the…

A: Solve the following

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: Let F(x, y, z) = 15x? + 12y2 + 10z?. Find the equation to the tangent plane to the level of surface…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A particle moves in the xy−plane, so that its coordinates at time t≥0 are x(t)=3t3−3t2, y(t)=20t2+2t…

A: Given

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

A:

Q: 6. Given the space curve r(t) = (t, 2et, e2t), find the tangential and normal components of…

A:

Q: When body is an equilibrium ,the net force is vanish ulgn O İhi O

A: when body is an equilibrium the net force is vanish

Q: use Eq. (3) to calculate the curvature function κ(t)  r(t) = (t−1, 1, t)

A: Solution:Given     r(t)=(t-1, 1,t)To find κ(t):κ(t)=r'(t)×r''(t)r'(t)3

Q: Find the outward flux across the domain D xi + yj + zk x2 +y? + z? F(x,v,z) = across the sphere x2…

A:

Q: Determine the acceleration (vector and magnitude) of the fluid particle occupying the point (-2, 1,…

A: The acceleration vector is,                              a =ax + ay +az  where…

Q: Suppose that over a certain region of space the electrical potential V is given by V(x, y, z) = x^2…

A:

Q: Exercise (2): Calculate fe xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to…

A: we have to following integral

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Consider M is the mass of the triangular plate bounded by the y-axis and both the lines. To find…

Q: The velocity components in the x and y directions in terms of stream function w is given by

A:

Q: A projectile with mass m is launched into the air on a parabolic trajectory. For t >0, its…

A: In the absence of drag or viscous force , the total Mechanical energy of projectile remain constant

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

A:

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A:

Q: find the flux of f=zk across the portion of the sphere x2+y2+z2=a2 in the first octant in the…

A: Given the field, F=zk The surface S is the portion of the sphere x2+y2+z2=a2 in the first octant in…

Q: Suppose that an equilateral plate that is 2 feet high is standing straight on the bottom of a 6 feet…

A: We will find force on horizontal slice of plate and then integrate it to find total force . 56u

Q: Let g(x,y,z)=2xe^y+yz^2. Use the gradient vector to find the equation of the tangent plane to the…

A: We will use definition

Q: are two linearly independer d'y 3dy equation dx? dx

A:

Q: write the line thraugh y S.0;?) (5,0, in the dircetion of 2 vcetor parametruc امپري؟

A:

Q: Write the equations of the tangent plane and the normal line to the surface y + In(xz) Z = at the…

A: I have appended the formula used in the solution part

Q: a. Find the equation of osculating plane to Z1 at t=0

A: A(0) = &lt; -2, 5, 4&gt;     ---(1)  B(t) = &lt; 3/5 cos t , 3/5 sin t , 4/5 &gt;    =&gt; B(0)  =…

Q: Suppose that over a certain region of space the electrical potential V is given by V (x, y, z) = 6x²…

A: We have to find the rate of change of V at point P in direction of v .

Q: Q, Solve he differnktial equntion by Laplace troms form. ý-y =t, yW=1, ý(0) =1

A: Note: According to Company Guidelines we are providing the answer of first question. Kindly post…

Q: A fluid has density 600 kg/m3 and flows with velocity ū = ri + y. measured in meters, and the…

A: Here we have, Velocity v→=xi^+yj^+zk^ where x,y, and z are measured in meters.  the equation of…

Q: Suppose n is a vector normal to the tangent plane of the surface F(x, y, z) = 0 at a point. How is n…

A: We have asked how a vector n which is normal to the tangent plane of the surface F(x,y,z)=0 at a…