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A gypsum mold used for slip casting has an average pore radius of Rc=0.5 mm. The average length of the pores in the wall of the mold is 3.2 cm. Assuming perfect wetting, viscosity of liquid to be 1.01 millipascal.sec, surface tension equal to 73 mN/m, determine the time it takes for the liquid to pass through the walls. Assuming the pore shape to be cylindrical, calculate the flow rate of liquid through each pore.

User Youss
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The time it takes for the liquid to pass through the walls can be calculated using the Washburn equation:

t = (ηLr^2)/(4σcosθ)

where:
- η is the viscosity of the liquid
- L is the average length of the pores
- r is the average pore radius
- σ is the surface tension
- θ is the contact angle between the liquid and the mold wall

Assuming perfect wetting, the contact angle is 0°, so cosθ = 1. Substituting the given values, we get:

t = (1.01 x 10^-3 Pa.s x 3.2 x 10^-2 m x (0.5 x 10^-3 m)^2)/(4 x 73 x 10^-3 N/m x 1)
t = 2.03 x 10^-4 s

Therefore, it takes approximately 0.203 ms for the liquid to pass through the walls.

The flow rate of liquid through each pore can be calculated using Poiseuille's law:

Q = πr^4ΔP/(8ηL)

where:
- Q is the flow rate
- ΔP is the pressure difference across the wall

Assuming the pressure difference across the wall is 1 atm, or 101325 Pa, we get:

Q = π(0.5 x 10^-3 m)^4 x 101325 Pa/(8 x 1.01 x 10^-3 Pa.s x 3.2 x 10^-2 m)
Q = 1.13 x 10^-10 m^3/s

Therefore, the flow rate of liquid through each pore is approximately 1.13 x 10^-10 m^3/s.
User Louis Langholtz
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