How to Calculate the Force Exerted by Water on a Hinged Gate?

[sita]

Homework Statement

http://www.pictureshoster.com/thumbnails/fzfnh5lyl6epxx11dmp_thumb.jpg

the gate is connected by a hinge at point A and a force holds it shut at point C

water density $$\rho$$=1000 kg/m$$^{3}$$

width of the gate is 1m (into page)

Homework Equations

F = $$\sqrt{F_{h}^{2} + F_{v}^{2}}$$
F = $$\rho$$ghA

The Attempt at a Solution

i'm guessing to find the force due to the water i have to look at the horizontal and vertical components.. but i haven't had an example before where the gate isn't just one straight line! nor one with water under the gate.. so I'm a bit lost as to what to do?

thanks for the help

 

[Q_Goest]

Hi sita,
Welcome to the board. Do you know how to find the resultant normal force on each section? You have 3 sections, so reduce the force on each section to a single resultant force. Once you do that, you can find moments around a single point as well as sum forces vertically and horizontally. Does that help?

 

[Mene]

I would first identify the problem and gather all relevant information provided. From the given image, it appears that the gate is being held shut by a force at point C and is connected to a hinge at point A. The water density is also given as 1000 kg/m^3 and the width of the gate is 1m.

Next, I would use the given equations to calculate the force exerted by the water on the gate. The first equation, F = \sqrt{F_{h}^{2} + F_{v}^{2}}, can be used to find the total force exerted by the water on the gate. This equation takes into account both the horizontal and vertical components of the force.

To calculate the horizontal force, we can use the equation F_h = \rhoghw, where \rho is the water density, g is the acceleration due to gravity, h is the height of the water, and w is the width of the gate. In this case, the width of the gate is 1m and the height of the water can be found by measuring the distance from the bottom of the gate to the surface of the water.

To calculate the vertical force, we can use the equation F_v = \rhogA, where A is the area of the gate. In this case, the area of the gate can be found by multiplying the width (1m) by the height (as calculated above).

Finally, we can use the first equation to find the total force exerted by the water on the gate. This total force will be a combination of both the horizontal and vertical forces.

It is important to note that the direction of the force will depend on the direction of the hinge and the direction of the force holding the gate shut at point C. The calculations above assume that the gate is being pushed towards the hinge at point A and held shut at point C.

In conclusion, the force exerted by the water on the gate can be calculated using the given equations and taking into account the direction of the force and the dimensions of the gate.