Solving Hydrostatic Forces with Integral or Volume/Weight?

[Link-]

I am actually trying to solve a problem from fluid mechanics. The especifications of the problem are on the attachment.

I can solve the problem easily by integration, but I'm not so sure if there is a vertical component of a force in the "dam" acting upward. There is a vertical component of the force acting upward?
If there is, there is another method to solve the problem without integration, using properties such as volume, specific weight... to find that vertical component?

 

[Dale]

I'm not sure what the various parts of your drawing represent. However, in general, pressure always acts normal to the surface. So if the normal vector of your surface at a given point has a vertical component then the pressure force will also have a vertical component. The easiest way to do something like this is to write an expression for the normal vector as a function of x (or y) and then use that in the integration.

 

[charng]

I would recommend using the integral method to solve this problem. This method is commonly used in fluid mechanics and is a reliable and accurate way to calculate hydrostatic forces. It takes into account the pressure distribution and the shape of the object, making it a more comprehensive approach.

Regarding the vertical component of the force, it is important to note that in hydrostatics, the pressure acts perpendicular to the surface of the object. Therefore, in this case, there would be a vertical component of the force acting upward. This component can be calculated by taking into account the specific weight of the fluid and the volume of the object.

While it is possible to use other properties such as volume and specific weight to calculate the vertical component, it may not be as accurate as using the integral method. Furthermore, the integral method provides a more comprehensive understanding of the forces acting on the object.

In conclusion, I would recommend using the integral method to solve this problem as it is a reliable and accurate approach in fluid mechanics. It takes into account all the necessary factors and provides a thorough understanding of the hydrostatic forces at play.