You need to design for the length, L of a capillary tube of diameter d=6mm conne

Question

You need to design for the length, L of a capillary tube of diameter d=6mm connected to a much larger diameter tank to continuously provide 30gm/s of cooling liquid flow to a computer chip's hot spot. (See adjacent figure.) The liquid is a low dielectric-constant fluid (a good electrical insulator) of viscosity coefficient 4gm/m/s. (Note that the pressure at stations 1 and 2 is of course atmospheric and assume that the tank is always full as it is continuously replenished.) Assuming in-viscid flow develop an expression for L then calculate it based on data provided. Develop an expression for L accounting for fictional effects but neglecting entrance effects, i.e. assume that the flow in the capillary tube is fully de'eloped. Then calculate L and compare to the inviscid approximation from ).

Explanation / Answer

Area A = 3.14/4*6^2 = 28.26 mm^2

Massflow rate m = rho*A*V

30*10^-3 = rho*V*28.26*10^-6

rho*V = 1061.6

Reynolds number Re = rho*V*D/u = 1061.6*6*10^-3 / (4*10^-3) = 1592.4

Since Re < 2300, flow is laminar.

Friction factor f = 64 / Re = 0.0402

dP = f*L/d*V^2 / (2g)

For rest of the problem, we need to have the figure which is missing.

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