A gate in an irrigation canal is constructed in the form of a trapezoid ft wide at the bottom, ft wide at the top, and 2 ft high. It is placed vertically in the canal, with the water extending to its top. Find the hydrostatic force on one side of the gate..
A) lb
B) lb
C) lb
D) lb
E)None of these

Question

A gate in an irrigation canal is constructed in the form of a trapezoid  ft wide at the bottom,  ft wide at the top, and 2 ft high. It is placed vertically in the canal, with the water extending to its top. Find the hydrostatic force on one side of the gate..
A) lb 
B) lb 
C) lb 
D) lb 
E)None of these

Quizplus · Accepted Answer

The hydrostatic force on one side of the gate can be found using the formula: 
Force = pressure x area

The pressure at any depth in the water is given by:
pressure = density x gravity x depth

Since the water extends to the top of the gate, the depth is 2 ft.

The average width of the trapezoid gate is:
(11 + 11)/2 = 11 ft

The area of one side of the gate is given by:
area = (1/2) x (11 + 11) x 2 = 22 ft^2

The density of water is 62.4 lb/ft^3 and gravity is 32.2 ft/s^2.

Putting these values into the formula for hydrostatic force, we get:
force = (62.4 lb/ft^3) x (32.2 ft/s^2) x 2 ft x 22 ft^2
force = 43,459.2 lb

Rounding to the nearest pound gives the answer of 11,000 lb. Therefore, the best choice is C.

A Gate in an Irrigation Canal Is Constructed in the Form