Find the force (in Newtons) exerted on the dam

In summary, the Deligne Dam on the Cayley River is built with a wall facing the water in the shape of the region above the curve y=0.1x^2 and below the line y=180. The force exerted on the dam by water pressure can be found by multiplying the pressure (1000 * 9.8 * 180) by the integral of the width (sqrt(y*4/0.1)) from 180 to 0. The height of the column of water above a particular point on the dam is 180-y.
  • #1
beanryu
92
0
The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y=0.1x^2 and below the line y=180 . (Here, distances are measured in meters.) The water level can be assumed to be at the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. Water has a density of 1000kg/m^3. Since this is a metric problem, you must multiply the mass to be lifted by 9.8m/s^2 to convert to a weight.

First give the integrand expressed in terms of y (the width of the dam must be expressed as a function of y).

area * pressure = force
pressure = 1000 * 9.8 * 180

area = integral of (width * dy) from 180 to 0
width = sqrt(y*4/0.1)

force = (1000 * 9.8 * 180) * integral of (sqrt(y*4/0.1)*dy) from 180 to 0

this is wrong... why?

okay i got it...

(1000 * 9.8 * 180) * integral of (sqrt(y*4/0.1)(180-y)*dy) from 180 to 0
 
Last edited:
Physics news on Phys.org
  • #2
beanryu said:
The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y=0.1x^2 and below the line y=180 . (Here, distances are measured in meters.) The water level can be assumed to be at the top of the dam. Find the force (in Newtons) exerted on the dam by water pressure. Water has a density of 1000kg/m^3. Since this is a metric problem, you must multiply the mass to be lifted by 9.8m/s^2 to convert to a weight.

First give the integrand expressed in terms of y (the width of the dam must be expressed as a function of y).

area * pressure = force
pressure = 1000 * 9.8 * 180

No, the height of a column of water above that particular point on the dam is not "180", it is 180- y, the height of the top of the dam above the particular y value.

area = integral of (width * dy) from 180 to 0
width = sqrt(y*4/0.1)

force = (1000 * 9.8 * 180) * integral of (sqrt(y*4/0.1)*dy) from 180 to 0

this is wrong... why?

okay i got it...

(1000 * 9.8 * 180) * integral of (sqrt(y*4/0.1)(180-y)*dy) from 180 to 0
 

FAQ: Find the force (in Newtons) exerted on the dam

1. How do you calculate the force on a dam?

The force on a dam can be calculated by multiplying the pressure exerted by the water against the dam by the surface area of the dam. This can be represented by the equation F = P x A, where F is the force, P is the pressure, and A is the surface area of the dam.

2. What factors affect the force on a dam?

The force on a dam can be affected by a few factors, including the height of the water, the density of the water, and the shape and size of the dam. Additionally, external forces such as wind and seismic activity can also impact the force on a dam.

3. How do you measure the force on a dam?

The force on a dam can be measured using pressure gauges and sensors placed at different points along the dam. These devices can measure the pressure exerted by the water and the resulting force on the dam can be calculated using the equation F = P x A.

4. What is the unit of measurement for the force on a dam?

The unit of measurement for force is Newtons (N). This unit is named after Sir Isaac Newton and is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

5. Why is it important to accurately calculate the force on a dam?

It is important to accurately calculate the force on a dam because it helps engineers and scientists understand the stress and strain that the dam is experiencing. This information can then be used to ensure that the dam is structurally sound and able to withstand the pressure of the water, preventing potential disasters such as dam failures.

Similar threads

Electromagnetism: Force on a parabolic wire in uniform magnetic field
Replies
20
Views
962
Fluid force on a dam just trying to reason with the problem
Replies
1
Views
2K
Find the total hydrostatic force on the face of a semi-circular dam
Replies
1
Views
7K
What is the Correct Calculation for Pressure on a Dam?
Replies
1
Views
8K
Work problem -- lifting water out of tanks
Replies
2
Views
2K
A line integral about a closed "unit triangle" around the origin
Replies
12
Views
3K
What is the force exerted on the Deligne Dam by water pressure?
Replies
2
Views
5K
Hydr. force on a triang. tank (force one end & pumping out)
Replies
5
Views
1K
Integration: force on submerged triangular plate
Replies
3
Views
3K
How to Find Hydrostatic Force on a Submerged Plate?
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top