Chapter 4, Problem 1FP

To determine

The mass flow of water

Explanation of Solution

Given:

The width of the rectangular tube $\left(B\right)$ is 60 mm.

The average velocity of the flow $\left(V\right)$  is 16 m/s.

The density of the water $\left({\rho }_w\right)$  is $1,000\text{kg}/{\text{m}}^{\text{3}}$.

The depth of flow $\left(y\right)$ is 50m m.

Calculation:

Calculate the depth of the tube perpendicular to the flow (D).

  $\begin{array}{c}D=y\sin \theta \\ D=50\text{ mm}\times \sin 60°\\ =50\text{ mm}\times \frac{1\text{ m}}{1000\text{ mm}}\times \sin 60°\\ =\text{0}\text{.043}\text{m}\end{array}$

Calculate the area of the rectangular tube A.

  $\begin{array}{c}A=B\times D\\ A=60\text{ mm}\times 0.043\\ =60\text{ mm}\times \frac{1\text{m}}{1000\text{ mm}}\times 0.043\\ =\text{0}\text{.00259}{\text{m}}^{\text{2}}\end{array}$

Calculate the mass flow $\dot{m}$.

  $\begin{array}{c}\dot{m}=\rho AV\\ \dot{m}=1,000\text{kg}/{\text{m}}^{\text{3}}\times 16\text{m}/\text{s}\times 16\text{m}/\text{s}\\ =41.6\text{kg}/\text{s}\end{array}$

Thus, the mass flow of water is $\underset{\_}{41.6\text{kg}/\text{s}}$.