Chapter 5, Problem 5.21P

(a)

Interpretation Introduction

Interpretation:

The velocity at the station $2$ is to be calculated.

Concept Introduction :

The fluid flows through a sluice gate between station $1\text{and}\text{2}$ . The density, height and velocity of the liquid and at station $1\text{and}\text{2}$ is given. The conservation of mass is applied to calculate the velocity at station $2$ .

The equation of conservation of mass is,

  ${\text{mass}}_{in}={\text{mass}}_{out}$

(b)

Interpretation Introduction

Interpretation:

The force per unit width to hold the sluice gate is to be calculated.

Concept Introduction :

The force required to hold the gate is calculated by applying the momentum balance equation.

According to the momentum balance equation, the summation of the forces is equal to the rate of change of momentum.

The momentum balance equation is,

  ${\displaystyle \sum F_x}={\displaystyle \underset{c.s}{\iint }\rho v_x\left(\overrightarrow{v}\cdot \overrightarrow{n}\right)}dA$