Repeat part (a) of Prob. 7–113, except instead of height h, find a functional relationship for the time scale t_rise needed for the liquid to climb up to its final height in the capillary tube.

Data from Problem 7–113

When a capillary tube of small diameter D is inserted into a container of liquid, the liquid rises to height h inside the tube (Fig. P7–113). h is a function of liquid density ρ, tube diameter D, gravitational constant g, contact angle Ф, and the surface tension σ_s of the liquid. 

(a) Generate a dimensionless relationship for h as a function of the given parameters.

(b) Compare your result to the exact analytical equation for h given in Chap. 2. Are your dimensional analysis results consistent with the exact equation? Discuss.

FIGURE P7–113

Transcribed Image Text:

Too P. σs -D h