Consider the rise of a liquid in a capillary tube as in Figure 2-36 in the textb

Question

Consider the rise of a liquid in a capillary tube as in Figure 2-36 in the textbook, for the simplified case of contact angle = 0. Suppose you don't know any physics about the problem. All you know is that capillary rise height h is a function of p, g. D). and sigma s. [D is the inner diameter of the capillary tube. ] Use dimensional analysis to generate a dimensionless relationship between the variables. Show all your steps. What kind of relationship (linear, quadratic, etc.) makes your result of Part (a) agree exactly with the known analytical solution (see Section 2-7 in the textbook)?

Explanation / Answer

DIMENSION OF (DENSITY)=KG/m^3

g=m/s^2

D=m

s=kg/s^2

NOW h*g*D*=m*(m/s^2)*m*(kg/m^3)=kg/s^2

s=kg/s^2

so,DIMENSIONALLY

S=hgD

h=s/gD

IT MAKES LINEAR RELATION SHIP WITH KNOWN ANALYTICAL SOLUTION WHICH IS h=(2s*cos)/gD

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