# Calculating Fluid Force of Triangle Submerged in Water

• Blonde1551
In summary, the problem involves finding the fluid force on a vertically submerged triangle with a base of 6 ft and height of 4 ft, submerged to a depth of 3 ft in a body of water. The equation used is W ∫ h(y) L(y), with h(y) = -y and L(y) = 2 (3/4(y+7)). After calculating, the result is 3244.8 lbs.
Blonde1551

## Homework Statement

Find the fluid force of a triangle with base of 6 ft and height of 4 ft submerged vertically into a body of water,vertex down, to a depth of 3 feet.

## Homework Equations

from c to d W h(y) L(y)

## The Attempt at a Solution

I set up the triangle on an x and y axis, splitting it down the middle. I made h(y) = -y and
L(y)= 2 (3/4(y+7)) (I found the equation of the line for the side of the triangle and multiplied it by 2). W is equal to 62.4

I set the problem up like this -6/4 x 62.4 times the integral from -7 to -3 of y(y+7).
When I integrated this I got 3244.8 lbs. I just want to know if I did this correctly. If not, please explain where I went wrong.

Looks like you got it to me.

The only thing unconventional to me is using -ve y in your set up. Usually in hydrostatic problems y is just taken as +ve in the down direction. Using your convention the force should have come out -ve mathematically. But as long as you are consistent it didn't matter.

## 1. How do you calculate the fluid force of a triangle submerged in water?

To calculate the fluid force of a triangle submerged in water, you will need to use the formula F = ρghA, where ρ is the density of water, g is the acceleration due to gravity, h is the height of the triangle submerged in water, and A is the area of the triangle. You can also use the formula F = ½ρghA, where h is the distance from the centroid of the triangle to the surface of the water.

## 2. What is the significance of calculating the fluid force of a triangle submerged in water?

Calculating the fluid force of a triangle submerged in water is important in understanding the behavior of objects in fluid environments. This calculation helps determine the pressure exerted on the triangle by the surrounding water, which can be useful in designing structures that will be submerged in water.

## 3. Can the fluid force of a triangle submerged in water be negative?

Yes, the fluid force of a triangle submerged in water can be negative if the triangle is oriented in a way that the fluid force is acting in the opposite direction of the positive coordinate system. This indicates that the water is pushing the triangle in the opposite direction of its motion.

## 4. How does the shape of the triangle affect the fluid force when submerged in water?

The shape of the triangle can affect the fluid force when submerged in water as it determines the area of the triangle that is in contact with the water. A larger area will result in a larger fluid force as there is more surface for the water to exert pressure on. Additionally, the shape of the triangle can also affect the distribution of the fluid force on the triangle.

## 5. Can the fluid force of a triangle submerged in water change over time?

Yes, the fluid force of a triangle submerged in water can change over time. This can occur if the water level changes, causing the height of the triangle submerged in water to change. Additionally, if the orientation of the triangle changes, the fluid force acting on it will also change. Furthermore, if the shape of the triangle is not uniform, the fluid force may also vary along its surface.

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