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Example 4: Derive an expression for the capillary height change $h$, for a fluid of surface tension $\sigma$ and contact angle $\phi$ between two parallel plates $W$ apart. Evaluate $h$ for water at 20°C ($\sigma$=0.0728 N/m) if $W$ = 0.5 mm. Solution: With (b) the width of the plates into the paper, the capillary forces on each wall together balance the weight of water held above the reservoir free surface: $hbpgW = 2(\sigma bcos\phi)$ $h = \frac{2(\sigma cos\phi)}{pgW}$ for water at 20°C ($\sigma$=0.0728 N/m, $\gamma$ = 9790 $\frac{N}{m^3}$) and $W$ = 0.5 mm. $h = \frac{2 \times (0.0728 \times cos(0))}{9790 \times 0.0005} = 0.03m = 30mm$ Q: Drive the expression for $h$ if the cross section area of the tube is square with length of $a$.

          Example 4: Derive an expression for the capillary height change $h$, for a fluid
of surface tension $\sigma$ and contact angle $\phi$ between two parallel plates $W$ apart.
Evaluate $h$ for water at 20°C ($\sigma$=0.0728 N/m) if $W$ = 0.5 mm.
Solution: With (b) the width of the plates into the paper, the capillary forces on
each wall together balance the weight of water held above the reservoir free
surface:
$hbpgW = 2(\sigma bcos\phi)$
$h = \frac{2(\sigma cos\phi)}{pgW}$
for water at 20°C ($\sigma$=0.0728 N/m, $\gamma$ = 9790 $\frac{N}{m^3}$) and $W$ = 0.5 mm.
$h = \frac{2 \times (0.0728 \times cos(0))}{9790 \times 0.0005} = 0.03m = 30mm$
Q: Drive the expression for $h$ if the cross section area of the tube is square with
length of $a$.

Example 4: Derive an expression for the capillary height change h, for a fluid
of surface tension σ and contact angle ϕ between two parallel plates W apart.
Evaluate h for water at 20°C (σ=0.0728 N/m) if W = 0.5 mm.
Solution: With (b) the width of the plates into the paper, the capillary forces on
each wall together balance the weight of water held above the reservoir free
surface:
hbpgW = 2(σ bcosϕ)
h = (2(σ cosϕ))/(pgW)
for water at 20°C (σ=0.0728 N/m, γ = 9790 (N)/(m^3)) and W = 0.5 mm.
h = (2 × (0.0728 × cos(0)))/(9790 × 0.0005) = 0.03m = 30mm
Q: Drive the expression for h if the cross section area of the tube is square with
length of a.

Added by Ines W.

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