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FLUID STATICS Learning Objectives

1). To evaluate the hydrostatic pressure loading acting on a body that is immersed in a liquid. 2). To determine the resultant of a given line, pressure, or

body load on a submerged body and to evaluate the reaction acting on the body that carries such a load.

3). To do an engineering estimate of the equivalent loading.

Assumptions 1). The liquid is incompressible, (i.e., = constant). 2). The hydrostatic pressure loading always acts normal to

any submerged surface, regardless of orientation. 3). The hydrostatic (gage) pressure at a point in a liquid is

proportional to the depth “h” below the free surface.

Hydrostatic Pressure Distribution p = hydrostatic (gage) pressure (pgage = pabs – patm)

= density of the liquid g = acceleration of gravity h = height below the free surface of the liquid

p = ρgh

Fluid Statics – Flat Surfaces Example 1

Given: The lower edge of gate AB in the triangular trough is supported by a series of pins. The upper edge is supported by 20 equally spaced cables along the 40 ft length of the trough.

Find:

a) Make a sketch of the pressure distribution on gate AB.

b) Determine the magnitude and location of an equivalent force for the

hydrostatic load of the water.

c) Determine the tension in a cable when the trough is filled to the top with water

(assume the specific weight of the water is given by ρg = 62.4 lbs/ft3).

Fluid Statics – Flat Surfaces Example 2

Given: The horizontal width of the gate at the bottom of the retaining wall is 6 ft. Assume the fluid is water with a specific weight given by ρg = 62.4 lbs/ft3.

Find:

a) Sketch the pressure distribution that is exerted on the gate by the water.

b) Determine a single force equivalent and its location on the gate.

Fluid Statics, Buoyancy Forces Group Quiz 1

Group #: ____________ Group Members: 1) ______________________________ (Present Only) Date: ______________ Period: _________ 2) ______________________________

3) ______________________________

4) ______________________________

Given: The dam shown has a pin support at A, a roller support at B and a water depth of 4 ft on one side. The width of the dam (the dimension into the page) is 8 ft. The specific weight (ρg) of the water is 62.4 lb/ft3.

Find: a) Draw a sketch of the dam showing a side view of the

pressure distributed across all three surfaces. b) Calculate a single force equivalent for each of the

three surfaces and draw a sketch showing the location of each of the equivalent forces.

c) Neglecting the weight of the dam, what are the reactions at A and B?

Solution: