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# COULD YOU PLEASE DO THIS NUMERICAL FOR ME!!

Asked by pukai7229 17th May 2018, 8:49 AM
Let us check the dimension of the given relation      h = (r×ρ×g)/(2S)

units of [ (r×ρ×g)/(2S) ] =  { (m×(kg/m3)×(m/s2) } / (N/m) = { (m×(kg/m3)×(m/s2) } / {( kg×m/s2)/m) = m-1
Checking the units gives that units of height as inverse of length. hence the given equation is not corrrect.

Correct equation is derived below

Let us consider a capillary tube of radius r is dipped in a liquid of density ρ, and there is a capillary rise h.

Weight of the liquid inside capillary tube = Voulme×density×g = πr2h×ρ×g .................(1)

This weight gives downward force. This downward force balanced by upward surface tension force.

Surface tension S is the force acting on the circumference of the top of the liquid surface . Hence total force  upwards is S×cosθ×2πr.
θ is the angle of contact. For liquid like water,  θ is very near to zero, so that we consider cosθ = 1.

Then S×2πr = πr2h×ρ×g;

By simplifying the above expression, we get    h = 2×S / (r×ρ×g)

Answered by Expert 17th May 2018, 3:09 PM
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