Answer to Question #198255 in Calculus for Ben

Question

Force due to Liquid Pressure 

Problem 1: A horizontal cylindrical pipe has a 4-ft inner diameter and is closed at one end by a circular gate that just fits over the pipe. If the pipe contains water at a depth of 3 ft, find the force on the gate due to water pressure.

Problem 2: A gate is in the form of a parabola 𝑥^2 = 8𝑦. Find the force on one side if it is submerged vertically with the focal chord (latus rectum) along the surface of water.

Problem 3: A gate is in the form of letter T with the vertical 2 ft wide and 4 ft high. The horizontal crosspiece is 6 ft long and 1 ft high. Find the force on one side if the gate is submerged vertically with the top of the crosspiece along the surface of water.

Problem 4: An automobile’s gasoline tank is in the shape of a right-circular cylinder of radius 8 in with a horizontal axis. Find the force on one end when the gasoline is 12 in deep if 0.39 oz / in^3 is the weight density of the gasoline.