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A large water trough is 19 m long and has ends shaped like inverted isosceles triangles, with a base of 12 m and height of 5 m. Water density is 1000 kg/m^3 and acceleration due to gravity is 9.8 m/s^2. Find the force on one end of the tank if the trough is filled to a point 1 m below the edge. If necessary, round your answer to the nearest Newton.

A large water trough is 19 m long and has ends shaped like inverted isosceles triangles, with a base of 12 m and height of 5 m. Water density is 1000 kg/m^3 and acceleration due to gravity is 9.8 m/s^2. Find the force on one end of the tank if the trough is filled to a point 1 m below the edge. If necessary, round your answer to the nearest Newton.

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A large water trough is 19 m long and has ends shaped like inverted isosceles triangles, with a base of 12 m and height of 5 m. Water density is 1000 kg/m^3 and acceleration due to gravity is 9.8 m/s^2. Find the force on one end of the tank if the trough is filled to a point 1 m below the edge. If necessary, round your answer to the nearest Newton.

Explanation & Steps

First define a coordinate system and origin. Coordinate system and origin will decide the variable and limits of integration in the calculations. Next, calculate the strip length using identity of similar triangles and use this length to determine area of the strip.

Hydrostatic pressure P acting on the object is given by \rho gd  where \rho is the density of the fluid and g is the gravitational acceleration. Finally constant pressure P acting on the surface with area A can be used to calculate force on the i^{th} strip, given by F = PA. Use appropriate limits on variable ‘x’ to determine force on one end of the tank.

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