Answer to Question #158396 in Mechanical Engineering for ad

Question #158396

Q12. Show that for the flow in the stokes law region, the terminal falling velocity of a spherical particle in a fluid medium may be given by vt = [4𝐷(πœŒπ‘ βˆ’πœŒ)𝑔3𝐢𝐷𝜌]1/2


1
Expert's answer
2021-02-10T01:08:47-0500

Answer

According to physics concept the

Terminal velocity: It is maximum constant velocity acquired by the body while falling freely in a viscous medium.

Now we can say

When a small spherical body falls freely through a viscous medium, three forces act on it.

(i) Weight of the body acting vertically downwards.

(ii) Upward thrust due to buoyancy equal to weight of liquid displaced.

So

"F_T+F_v=W"

"\\frac{4\\pi r^3 \\rho_s g}{3}+6\\pi\\eta v_t=\\frac{4\\pi r^3 \\rho g}{3}"

We get

"v_t=\\frac{2D^2(\\rho-\\rho_s)g }{9\\eta}"

Now putting above conditions

We get

"v_t=[4D(\\rho_s-\\rho) g3CD\\rho]^\\frac{1}{2}"


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