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9. A tube with length $L$ connects two reservoirs which contain salt waters. The cross-section (yz-direction) of the tube is so small so we can assume that the concentration of the salt water is same for any point on a cross-section. Let the concentration of the salt water in the tube be $c(t, x)$, $0 < x < L$. We assume that the diffusion of the salt is one-dimensional in the tube: $\frac{\partial c}{\partial t} = D \frac{\partial^2 c}{\partial x^2}$ Determine the boundary and initial conditions according to the following setups: (1.66)

          9. A tube with length $L$ connects two reservoirs which contain salt waters. The cross-section
(yz-direction) of the tube is so small so we can assume that the concentration of the salt
water is same for any point on a cross-section. Let the concentration of the salt water in the
tube be $c(t, x)$, $0 < x < L$. We assume that the diffusion of the salt is one-dimensional in the
tube:
$\frac{\partial c}{\partial t} = D \frac{\partial^2 c}{\partial x^2}$
Determine the boundary and initial conditions according to the following setups:
(1.66)

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9. A tube with length L connects two reservoirs which contain salt waters. The cross-section
(yz-direction) of the tube is so small so we can assume that the concentration of the salt
water is same for any point on a cross-section. Let the concentration of the salt water in the
tube be c(t, x), 0 < x < L. We assume that the diffusion of the salt is one-dimensional in the
tube:
(∂ c)/(∂ t) = D (∂^2 c)/(∂ x^2)
Determine the boundary and initial conditions according to the following setups:
(1.66)

Added by Francisca K.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/21/2023

Step 1

Boundary conditions: - At x = 0: The concentration of saltwater is given as c(t, x=0) << L. This means that the concentration at the left end of the tube is much lower than the concentration in the reservoirs. Therefore, we can assume that there is no salt Show more…

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A tube with length L connects two reservoirs which contain saltwater. The cross-section in the yz-direction of the tube is so small that we can assume the concentration of the saltwater is the same for any point on a cross-section. Let the concentration of the saltwater in the tube be c(t,x=0)<<L. We assume that the diffusion of the salt is one-dimensional in the tube: âˆ‚c/âˆ‚t = D âˆ‚Â²c/âˆ‚xÂ². Determine the boundary and initial conditions according to the following setups:

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