- #1

- 3,003

- 2

## Homework Statement

Water flows with a speed

*v*down a rectangular pipe of dimensions

*s*and

*l*as shown. What is the rate [itex]\Phi=volume\, per\, unit\, time [/itex]

at which water accumulates in the bucket?

## Homework Equations

[itex]\Phi=\int_S\mathbf{v}\cdot d\mathbf{a}[/itex]

## The Attempt at a Solution

I am confused as to how to compute this integral. I do not see how could use the divergence theorem to simplify it since I only have the dimensions of the 2-dim surface of the rectangular pipe.

I am not sure how to evaluate the surface integral based solely on its definition. Can someone help to get me started?

Do I just use the definition [itex]\Phi=\int_S\mathbf{v}\cdot d\mathbf{a}[/itex] for this?