In a certain region of the atmosphere, the pressure is given as a function of x, y and z
Consider a fluid moving in this pressure field. The position of the fluid particle is a function of time and given by
The symbols a, b, H, P and U represent constants.
-Find the wind components u, v, and w ?
-Find the total derivative dp dt according to x, y, z and t. ?
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- Find Local acceleration ?
- Find The advection ?
Thanks Advance
In a certain region of the atmosphere, the pressure is given as a function of x,...
Given a horizontal velocity vector V~ = 3xy^4 − 3x^5 y^3 , a temperature function of ~T = 1x^3 y^2 z^2 , and a pressure function of ~p = -3x^2yz^2 , please complete the following: (a) Determine the geostrophic wind vector Vg (b) Determine the temperature advection (c) Determine the velocity divergence
57. Find the total derivative dz/dt, given (a) z = x^2− 8xy − y^3 , where x = 3t and y = 1 − t. (b) z = f(x, y, t), where x = a + bt, and y = c + k
horizontal position, x, of a particle as a function of time is given by the equation xo + vo t + ½ at' , where xa vo and ao are constants. Find the velocity as a function of time. (2) Ifx0 2.0 m and vo 2.0 m/s and ao 1.0 m/s, find the acceleration of the particle in problem (1) at the time t-10.0 s
Question 5 [12 10 22 marks] (a) In a given inertial reference frame, S', consider a region of space where there is a uniform and constant electric field, E', and zero magnetic field, i.e. B' = 0. The frame S' moves with respect to an observer, in another frame S, with velocity v. Write an expression for the electric field, E, observed in S? Clearly explain any notation (i) and new quantities introduced Write an expression for the magnetic field,...
Mechanics. Need help with c) and d) 1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...
Suppose the atmosphere has its pressure given by p ( z ) = p 0 e ^ − z / H with p 0 = 1 atm and T ( z = 0 ) = 273 K. Now suppose a 1 kg parcel is lifted adiabatically one scale height H . How much work does the parcel do on the environment in the process? What is the change in its specific internal energy, u ?
Please do the parts in the given order tyā (x,y)メ(0,0) (x,y)= (0,0). if if 1 (d) Given the unit vector u-( find the directional derivative of f(x, y) at the 리지, ,- point (to,m) = (0,0), in the direction of the vector a. (e) Find the gradient of f(x, y) at the point (zo,o) (0,0) (c) Find the equation of the tangent plane to the graph of the function z -f(x, y) at the point (x,y,z) (1,0,0). tyā (x,y)メ(0,0) (x,y)=...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
17. Given f(x, y, z) = x^yz -- xyz', P(2,-1,1) and vector v =<1,0,1 >. Find i. the directional derivative of the function at the point P in the direction of v. ii. the maximum rate of change of f.
Just letter answer is good, thank you. 1. Given f(x,y) = 10r4y2-1lys, find fry(z, s). Q) 2. The graph of g'(x) is shown in figure. If g(3) 2 then what is the value of g(5)? g'(x) A. 2.0 B. 1.5 C. 2.5 6 12 3 D. 3.0 dy-r + si dx sin (2x) er 3. Find the general solution to the differential equation: B. 2x + 2 cos (r)-4e-4x + C D. none of the above llutant spilled on the...