Problem on Vertical Triangular Plate Immersed in Oil - Fluid Mechanics 1

TL;DR

Calculate the total pressure and center of pressure on a vertical triangular plate immersed in oil.

Transcript

hello friends here in this video we will see a problem in which there is a vertical triangular plate which is immersed in oil for that we have a question here i'll mark this question determine the total pressure and center of pressure on an isosceles triangular plate of base 4 meter when it is immersed vertically in an oil of specific gravity 0.9 t... Read More

Key Insights

• 🛢️ The specific gravity of the oil determines its density, which is necessary for calculations.
• 🍽️ The total pressure on the plate can be calculated using the hydrostatic force formula.
• 🍽️ The center of pressure is located at a distance of one-third of the height of the plate from the base.

Questions & Answers

Q: What is the total pressure on the vertical triangular plate?

The total pressure, also known as hydrostatic force, can be calculated using the formula f = ρghA, where ρ is the density of the oil, g is the gravitational acceleration, A is the area of the plate, and h is the height of the hydrostatic force.

Q: How do you calculate the area of the triangular plate?

The area of an isosceles triangular plate can be found using the formula A = 1/2 * base * height. In this case, the base and height are both given as 4 meters, resulting in an area of 8 square meters.

Q: What is the center of pressure?

The center of pressure is the point at which the hydrostatic force acts on the plate. It can be determined using the formula h* = (IG / A) * h bar + h bar, where IG is the moment of inertia, A is the area of the plate, h bar is the distance of the centroid from the free surface, and h is the height of the hydrostatic force.

Q: How do you calculate the moment of inertia for the triangular plate?

The moment of inertia for a triangular plate about its centroid can be found using the formula IG = (bh^3) / 36, where b is the base length and h is the height of the plate. In this case, the base length and height are both 4 meters, resulting in a moment of inertia of 7.11 m^4.

Summary & Key Takeaways

• The problem involves determining the total pressure and center of pressure on a vertical triangular plate in oil.

• The plate has a base of 4 meters and a height of 4 meters, coinciding with the free surface of the oil.

• The specific gravity of the oil is given as 0.9, allowing the calculation of the oil's density as 900 kg/m^3.