# Calculate the resultant thrust and overturning moment

• Taidhg
In summary, the problem involves a vertical retaining gate in a dry dock with water on one side at a depth of 21 meters. The gate is 2 meters wide and 24 meters high, with a density of 1030 Kg/m3 for seawater. The task is to calculate the retaining force at the middle of the free upper edge of the gate to keep it shut in the vertical position. The equations needed to solve this problem are hydrostatic pressure, force, thrust force, and overturning moment. The thickness of the gate is irrelevant and there is no provided diagram. A possible solution involves placing the hinge at the center of the door thickness to determine the torque due to water pressure.
Taidhg

## Homework Statement

A vertical retaining gate 2metres X 24metres hinged about the bottom edge of a dry dock has water to a depth of 21 metres on one side. Calculate the Retaining Force at the middle of the free upper edge of the gate to keep it shut in the vertical position. With the density of seawater being 1030Kg/m3.

## Homework Equations

Hydrostatic pressure = D*g*h
Force = P*A
Thrust force = D*g*(h/2)*A
Overturning moment = Thrustforce*(h/3)

## The Attempt at a Solution

I am sorry I really don't understand this question.

Is this a picture of the problem? It seems to me that the weight and density of the gate is needed?

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Spinnor said:
View attachment 235477

Is this a picture of the problem?
I wasn't provided with a diagram however that is the same as the one I produced

Taidhg said:
I wasn't provided with a diagram however that is the same as the one I produced

I thought the thickness of the gate was 2m. The height I guess is 2 meters, the width is 24, and the gates thickness is small. You need to integrate the total torque on the gate and equate that with 2xF ?

I would be wrong. The height must be 24m and the width 2m which makes for a very tall and narrow gate. Now I'm confused also.

The gate is 2 meters in width, 24 meters high, and its thickness is irrelevant. Think about how you might calculate the torque about the hinge's axis due to the water pressure.

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gneill said:
and its thickness is irrelevant

If it is thick then its weight might contribute a torque. But that info was not given.

Spinnor said:
If it is thick then its weight might contribute a torque. But that info was not given.
Place the hinge in the center of the door thickness. Problem solved

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Spinnor

## What does "calculate the resultant thrust and overturning moment" mean?

"Calculate the resultant thrust and overturning moment" refers to determining the combined force and torque exerted on a structure or object by a fluid, such as air or water, in a particular direction. This calculation is important for designing and analyzing structures that are exposed to fluid flow, such as airplanes, ships, and offshore platforms.

## What factors affect the resultant thrust and overturning moment?

The resultant thrust and overturning moment are affected by several factors, including the shape and size of the object, the velocity and direction of the fluid flow, and the properties of the fluid itself, such as density and viscosity. The angle at which the object is positioned relative to the fluid flow also plays a significant role.

## How is the resultant thrust and overturning moment calculated?

The resultant thrust and overturning moment can be calculated using the principles of fluid mechanics, specifically Bernoulli's equation and the concept of momentum. These equations take into account the variables mentioned in the previous question, and can be solved using mathematical methods or computational fluid dynamics (CFD) simulations.

## What is the significance of knowing the resultant thrust and overturning moment?

Knowing the resultant thrust and overturning moment is crucial for ensuring the structural integrity and stability of objects exposed to fluid flow. It helps engineers and scientists design and optimize structures to withstand the forces and moments exerted by fluid flow, minimizing the risk of failure or damage.

## Can the resultant thrust and overturning moment change over time?

Yes, the resultant thrust and overturning moment can change over time as the fluid flow conditions change. This is particularly important for dynamic structures, such as aircraft and ships, where the fluid flow and resulting forces and moments can vary significantly during operation. Continuous monitoring and analysis of these values are necessary for safe and efficient operation.

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