Consider a flow field where the density (kg/m3) is given by p(1,0,,t) = 2*22*(1 - ((r*t)/238)2...
2014/B5 (a) Draw skecthes to illustrate R, 0 and z coordinate curves for the case of cylindrical polar coordinates (b) Show that the gradient of a scalar field, p, can be expressed in terms of curvilinear coordinates u1, u2 and us, of an orthogonal coordinate system as where h, Idr/dul. Hence obtain a formula for Vip in cylindrical polar coordinates. (c) Evaluate dp/ds, the rate of change of φ with distance, for the field φ-R, cost) at the point R...
Consider the flow field with velocity given by: V = [A(y2-x2)-Bx] i + [2Axy+By] j, where A = 4 m-1s -1 and B = 4 m-1s -1. The coordinates are measured in meters. The density is 1,000 kg/m3, and gravity acts in the negative y-direction Calculate the acceleration of a fluid particle and the pressure gradient at point (x, y) = (1, 1).
JI,) a steady current density J = Ê Jer,p) OCR-), where Ol B-r) is the Heaviside O-function, flows in a cylindrical wire of radius R with a central axis along the z-axis of coordinates, set up the piot-Savart integral for the magnetic field Br. 63) at a general field point P. Your integral should have sto vector symbols Cepoept for rectangular unit vectors
Please help me. i didnt understand those formulas. can you please explain them. thanks. Problem 3.25 A vector field is given in cylindrical coordinates by Point P(2, T,3) is located on the surface of the cylinder described by r-2. At point P find (a) the vector component of E perpendicular to the cylinder, (b) the vector component of E tangential to the cylinder. Can anyone please tell me where does these formulas come from and also is there any formulas...
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proportional to the distance from P to the origin and 8(o, 3,02 15 pts] (0, 1,0)-2/m3 from P to the origin and Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2...
Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1 m/s, B = 1 s−1, and the coordinates are measured in meters. Obtain expressions forthe velocity field and the stream function. Using water as the working fluid, calculate the pressure difference between the origin and the point (x,y) = (1,2). What is the volume flow rate (per unit depth) between streamlines passing through these two points?
Problem 2 (6 points): Consider a solid sphere of radius R and uniform charge density p. Letr be the distance from the center of the sphere. It is helpful now to remind yourself what o(r) and E(F) are for this charge configuration. (a) Given the electric field E for the sphere, verify explicitly that XE = 0, both for r <R and r>R (3 points) (b) Show that V20= -p/c "CR T>R by expressing the electric potential o(r) in Cartesian...
(a) Let L and L' be two lines in R3. 1:*2 =12-21 Lt -1 5 -2 -1 2-5 -4. Determine if the lines intersect at a point. If the , write down the three coordinates of the intersection point in the three boxes below. If they do not, enter the three letters D, N, E, one in each box below (for Does NotExist) (b) An insect is flying along a path r(x,y,z) = (x(t), y(t), z(t)) in a room where...
(1 point) A solid conductor Occupies the cylindrical region p <b, o Szsh, where b = 6 mm and h= 20 m. A potential difference of 0.16 Volts between the ends at z = 0m and z = 20 m drives a steady current in the direction a,, and this produces a magnetic field intensity inside the conductor given (in units of A/m') by H = Hop-ap; H = 4 x 10. (a) Find the total resistance between z =...
with a flowrate of 10. kg/s. Energy-related values for streams are given bel p. Specific InternalEnerg Specifi-Enthal ykl kgー specific-oumc,ーーーーーーーーー -kl kg 1.00 ー Entering Leaving 0.00101 210 2600 211 20.0 0.501 2800 The amount of heat needed is closest to which value (show your work): 2600 kJ/s 28000 kJ/s 23900 kJ/s 25890 kJ/s q. An object is being cooled from an initial temperature of 300°C by contact with a fluid at 100°C. The rate of change in temperature for...