Question

Two glass tubes diameter 2 and 4 mm respectively, are attached to the side of a water tank to measure the level inside the tank, (surface tension = 0.074N/m)

Use this information to express the c apillary rise in the tube in the form h= mr + c where m and c are constants and r is the tube radius and hence determine the ideal tube diameter

Answer 1

$h_1 = \dfrac{2\sigma \cos\theta}{\rho gr} = \dfrac{2×0.074× (1)}{10^3×10×2×10^{-3}}$

$=0.0074m$

$h_2= \dfrac{2\sigma\ cos\theta}{\rho gr} = \dfrac{2×0.074×(\approx 1)}{10^3×10×4×10^{-3}}$

$=0.0037m$

$0.0074 = 0.002m + c\\ 0.0037= 0.004m+c$

$c=0.0111 \ \ m=−1.85$

$\therefore$ The final equation is;

$h=-1.85r + 0.0111$