In Exercises 25-28, a net is dipped in a river. Determine the flow rate of water across the net if the velocity vector...
In Exercises 25-28, a net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v and the net is described by the given equations. 26. v = (x _ y, z + y 4, z~ ), net given by y = I-x2-z2, y 0, oriented in the positive y-direction
In Exercises 25-28, a net is dipped in a river. Determine the flow rate of...
2. Determine whether there is a potential function for the vector field V= <yz, xz, xy>. You may use any legitimate method but you must justify your claim. If it there is a potential function, then find it and use it to evaluate the line integral ſ v.dr along the curve r(t) = <V7,4-4,6+1>ifor Osts 4. [10] 4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n...
H08.2 (2 points) Given the vector velocity field V(x, y, z, t) = 4t i + xz j + 2ty3 k a) Is this a valid incompressible flow field? b) Is this flow field irrotational?
Calculate the flow of the vector field F (picture) across the
surface of the solid W defined by the paraboloid z = 4-x^2-y^2 and
the xy plane, with normal outside W
F(x, y, z) = (x3,2xz2, 3y2z)
4. Suppose S is the surface z= x² + 4y? Tying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V- <y; -xz,xz> [12]
(25 %) Q4. A vector field is given as v=e"’i+e+*+j+evk a) Determine the curl of this vector field b) Determine the divergence of this vector field c) If this vector field shows a flow field, explain if the flow is rotational or irrotational. Also, explain if the flow is compressible or incompressible. d) Compute the rate of change of Q(x, y, z) at Po in the direction of r, where P(x, y,z)=2xy + xe”; Po = (-2,1, 6) and r=-2i+j+6k
For an imcomprresible fluid -y- direction velocity component on
(x,y) plane given . İn this statement a
and v constant.For the flow area of this fluid find the vortex
vector of -z- direction component.? Note:X=0 for
U(x,y)=0
xy 2aV- = (و ,) ( +y)
4. Suppose S is the surface z= x² + 4y’, lying beneath the plane z=1. Orient S by taking the inner normal n to pointing in the positive k direction. Calculate the flux integral across S in the direction n for the velocity field of a gas given by V= <y,-X2,xz'>[12]
Velocity in xy-Plane position in the xy plane is given by the vector (ct 4dtt)i +(2ct? -d')j, where c and d are positive c FInd the expression for the x-component of the velocity (for time t > 0) when the in the z-direction. You should express your answer in terms of the variables c and d. Find the n for the y component of the velocity (for timet 0) when the particle is moving in the y-direction. D
The velocity field of a flow is given by V = (2+1) x y2 i + (3+2) t j m/s where x and y is in meter and t in seconds. Determine the following at point (1, 2) and t= 3 s: 1. The fluid speed. 2. The angle between the velocity vector and the positive x 3. Locations (if avaliable) of any stagnation point for this flow field? 4. The local acceleration, then classiffy the flow . 5. The...