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3. How is the QGPV equation modified if we assume that the f...

3. How is the QGPV equation modified if we assume that the flow is exactly geostrophic (Hint: Re-derive the QGPV equation from the final lecture, i.e., the last equation on the website lecture notes file 7-review.pdf, assuming zero ageostrophic velocity.) 4. Determine whether the absolute vor...

Problem 2. Pipe with constant diameter d is rotating with a...

Problem 2. Pipe with constant diameter d is rotating with angular velocity Q around axis perpendicular to the free surface together with a pump mounted on it (see Figure). Given: R, Ho, H1, H2 atmospheric pressure Par density of the fluid P, gravitational acceleration g, power of the pump engine ...

FORCE ON AN INFINITESIMAL DIPOLE (Dielectrophoresis) Elect...

FORCE ON AN INFINITESIMAL DIPOLE (Dielectrophoresis) Electric force on dipole as a function of dipole moment Derivation of electric potential field due to a finite dipole Derivation of the effective dipole moment of a dielectric sphere in a dielectric medium (applying the correct boundary co...

A rocket sled which initially weighs Mo = 750 kg accelerates...

A rocket sled which initially weighs Mo = 750 kg accelerates from rests on a level track where there are no aerodynamic drag and rolling resistance. The rocket burns fuel at a constant rate of m = 25 kg/s and the exit speed of the exhaust gas relative to the sled is Ve = 1750 m/s. Calculate the (a) ...

Discuss in detail the limit a 0 in the cases when T is O(b...

Discuss in detail the limit a 0 in the cases when T is O(b) and when R = r/a is O(1). Also discuss in detail the limit a b. Give the shear stress at T = a for each limit. Concentric circular cross-sections: Steady flow a = 0. Try an axisymmetric solution r=b So(ru')'=-Gr/p. - ru'=-Gr²...

1) Consider the torque exerted by the surface forces on a f...

1) Consider the torque exerted by the surface forces on a fluid element Q with respect to a point O. The i-th component of the torque is given by: XX (o.n) . dS = ds. Here x is the coordinate of a surface element dS from the point O, b is the value of the stress tensor at x and n is the unit out...

2) Use cylindrical coordinates and obtain vorticity for an i...

2) Use cylindrical coordinates and obtain vorticity for an ideal vortex whose circumferential velocity is given by Vo = 1/2 r 2mt where F is a constant. Also compute the vorticity in a vortex flow given by Vo = F 2 where F and V are constants. 4) Let velocity gradient tensor at a point in a f...

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