# Fluid Mechanics problem

1. May 12, 2007

### Dafe

1. The problem statement, all variables and given/known data

How big must the external force be so that the speed u remains constant at 5m/s?

2. Relevant equations

Newton's second:

$$\sum\overrightarrow{F}=\overrightarrow{F_B}+\overrightarrow{F_S}= \frac{\partial}{\partial t}\int_{CV} \overrightarrow{V}\rho dV+\int_{CS} \overrightarrow{V}\rho \overrightarrow{V} \overrightarrow{dA}$$

3. The attempt at a solution

Assuming:
(2) Incompressible Flow
(3) Uniform flow at each section where fluid crosses the CV boundaries
(4) No body force (?)

I shorten it to :

$$\overrightarrow{F_{SX}}= \int_{CS} u \rho \overrightarrow{V} \overrightarrow{dA}$$

$$F_R=u|\rho V A| + F_N \mu_k$$

After inserting the given values I get

$$F_R=897,15N$$

- I'm not sure at all if I'm thinking correctly. I would really appreciate if someone could check my answer. Thanks!