Math Problem Statement

The isosceles triangular plate shown here is submerged vertically

22

ft below the surface of a freshwater lake.

a. Find the fluid force against one face of the plate.

b. What would be the fluid force on one side of the plate if the water were seawater instead of​ freshwater?

Surface Level6 ft6 ft2 ft

​(The triangle is not shown to​ scale.)

Question content area bottom

Part 1

a. Establish a coordinate system to work in by placing the origin at the​ plate's bottom vertex and running the​ y-axis upward along the​ plate's axis of symmetry. Assuming the triangle is submerged in​ freshwater, set up the integral that represents the fluid force against one face of the plate.

Integral from 0 to nothing left parenthesis nothing right parenthesis dy

Solution

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Math Problem Analysis

Mathematical Concepts

Fluid Mechanics
Calculus
Hydrostatic Pressure

Formulas

Fluid force = ∫[a to b] ρ * g * (depth function) * (width function) dy
Hydrostatic pressure formula: P = ρ * g * h

Theorems

Fundamental Theorem of Calculus
Principle of Hydrostatic Pressure

Suitable Grade Level

College-Level Calculus or Physics