I think what you mean is "perpendicular to the surface" rather than "vertical to the surface." Abuh11, to elaborate, the pressure at any depth is acting in the direction perpendicular to the surface. So you need to determine the pressure at each depth, multiply by the differential area involved, and add the forces vectorially (i.e., integrate over the arc of the surface).theodoros.mihos said:
Chestermiller said:
Chestermiller said:
Do you know how to find the volume of this water using geometry or calculus?abuh11 said:
Chestermiller said:
OK. From geometry, what is the volume of water directly under the gate.abuh11 said:
Chestermiller said:
I asked you for the volume of liquid below the gate. This is a geometry question, not a physics question. This is just the first step in getting to the answer you want. If you 're not willing to be patient, I won't be able to help you. This is part of how we determine the vertical component of force on the gate.abuh11 said:
Chestermiller said:
insightful said:
Ok, i done that. I got A and B now, what should i do with these numbers now?Chestermiller said:
Area B can get you to the volume of water displaced, right?abuh11 said:
insightful said:
Not really. What are the angles of triangle A? What is the area of the sector of the circle (A+B)?abuh11 said:
insightful said:
Hmm...a right triangle with two of the sides known...you've had trigonometry, right?abuh11 said:
yay. I manged to figure it out using your diagram and information. Thanks a lot.insightful said:
An interesting problem; I enjoyed working on it.abuh11 said:
insightful said:
The hydrostatic force on a submerged curved surface is calculated by multiplying the pressure at a given depth by the projected area of the curved surface. The pressure at a given depth can be calculated using the equation P = ρgh, where P is pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the fluid.
The hydrostatic force on a submerged curved surface is affected by the density of the fluid, the acceleration due to gravity, and the shape and orientation of the curved surface. The depth of the fluid and the shape of the curved surface also play a role in determining the magnitude and direction of the force.
The orientation of a curved surface can greatly affect the hydrostatic force. If the curved surface is horizontal, the force will be perpendicular to the surface. If the curved surface is vertical, the force will be parallel to the surface. The orientation of the curved surface can also affect the magnitude of the force, as a more angled surface will have a larger projected area and therefore a larger force.
Hydrostatic forces on submerged curved surfaces are important to understand in fields such as fluid mechanics, engineering, and hydrology. They play a crucial role in determining the stability and equilibrium of structures, such as dams, ships, and submarines. Understanding these forces is also important in designing and constructing hydraulic systems, such as pipes, pumps, and turbines.
Yes, the hydrostatic force on a submerged curved surface can be negative. This occurs when the curved surface is oriented in such a way that the force is acting in the opposite direction of the applied pressure. This can happen, for example, when the curved surface is concave and the pressure is acting from the outside of the curve. In this case, the force will be negative and will push the curved surface inwards.
