Chapter 2, Problem 2.19P

(a)

Interpretation Introduction

Interpretation:

The minimum height h for which the gate with rectangular cross section with rotate in clockwise direction is to be determined.

Concept Introduction:

The force $\left(F\right)$

acting on a surface due to a fluid above it is defined as:

  $F=\rho gzA$ ......... (1)

Here, $\rho$ is the density of the fluid with height $z$ , $A$ is the area of the surface, and g is the acceleration due to gravity.

Moment of force $\left(M\right)$

is the effect of the force applied at a particular distance from the axis of rotation on a rotational system which leads to its rotation. Mathematically it is written as:

  $M=F\cdot d$ ......... (2)

Here, $d$ is the perpendicular distance from the axis at which the force is applied.

(b)

Interpretation Introduction

Interpretation:

The minimum height h for which the gate with triangular cross section with rotate in clockwise direction is to be determined.

Concept Introduction:

The force $\left(F\right)$

acting on a surface due to a fluid above it is defined as:

  $F=\rho gzA$ ......... (1)

Here, $\rho$ is the density of the fluid with height $z$ , $A$ is the area of the surface, and g is the acceleration due to gravity.

Moment of force $\left(M\right)$

is the effect of the force applied at a particular distance from the axis of rotation on a rotational system which leads to its rotation. Mathematically it is written as:

  $M=F\cdot d$ ......... (2)

Here, $d$ is the perpendicular distance from the axis at which the force is applied.