# Fluid Statics: Calculate Moment on Rectangular Gate Hinged on Upper Edge

• physocs1
In summary, the conversation discusses a rectangular gate in a channel that separates a fresh-water lake and a salt-water tidal basin. The gate is hinged at its upper edge and the question asks for the moment on the shaft at a certain salt-water level. Three equations are provided to calculate the forces on the gate, and the solution involves using the equation for hydrostatic pressure and solving for the moment using the sum of moments. There is also confusion about which equation to use and how the height of the gate was calculated.
physocs1

## Homework Statement

The rectangular gate shown in section is 3 m long (perpendicular to the paper) and is hinged about its upper edge B. The gate divides a channel leading to a fresh-water lake on the left and a salt-water tidal basin on the right. Calculate the moment, M, on the shaft of the gate at H required to prevent the gate from opening when the salt-water level drops to h = 1 m. Take the density of salt water 1050 kg/m3

## Homework Equations

1. Force=rho*g*v
2. F=gamma*h*a
3.R= rho*g*h*a
Where gamma = specific weight of liquid
Where R=hydrostatic pressure

## The Attempt at a Solution

Calculate Both forces acting on rectangle gate. Then solve for the moment
Using sum of moments

****
I am confused on which equation to use. I want to use 3. since its a flat surface but I confused whether to use gravity in the equation?

[/B]

On another note: In the attached png. I am confused on they calculated "3/2" for the height
I am thinking if its the centroid?

#### Attachments

• Capture.PNG
65.9 KB · Views: 619

## 1. What is fluid statics?

Fluid statics is the study of fluids at rest, where there is no motion or flow. It focuses on the behavior and properties of fluids when they are not in motion, and how they interact with solid surfaces.

## 2. How do you calculate the moment on a rectangular gate hinged on the upper edge?

The moment on a rectangular gate hinged on the upper edge can be calculated by multiplying the force acting on the gate by the distance from the hinge to the line of action of the force. This is known as the moment arm. The formula for moment is M = Fd, where M is the moment, F is the force, and d is the moment arm.

## 3. What factors affect the moment on a rectangular gate?

The moment on a rectangular gate can be affected by several factors, including the force acting on the gate, the distance of the force from the hinge, the shape and size of the gate, and the fluid properties such as density and viscosity.

## 4. How does the location of the hinge affect the moment on a rectangular gate?

The location of the hinge can greatly affect the moment on a rectangular gate. If the hinge is placed closer to the line of action of the force, the moment arm will be shorter and the moment will be smaller. If the hinge is placed farther away, the moment arm will be longer and the moment will be greater.

## 5. What is the significance of calculating the moment on a rectangular gate in fluid statics?

Calculating the moment on a rectangular gate is important in understanding the stability and equilibrium of the gate. It helps determine whether the gate will remain in place or if it will rotate or move due to the forces acting on it. This information is crucial in designing and engineering structures that involve fluid interactions, such as dams, locks, and water tanks.

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