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Pervious Lecture Contents 2

1. Characteristics of Pressure

2. Pressure of fluid at rest

3. Measurement of Pressure

Simple manometers

Differential manometers

Mechanical gauge

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Fayoum University

Faculty of Engineering

Mechanical Engineering Dept.

Dr. Emad M. Saad Mechanical Engineering Dept.

Faculty of Engineering

Fayoum University

Fluid Statics

Lecture (3)

on

By

2015 - 2016

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Hydrostatic Forces on Completely Submerged Plane Surfaces

Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

5

Hydrostatic Forces on Completely Submerged Plane Surfaces

Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

x

y

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Hydrostatic Forces on Completely Submerged Plane Surfaces

Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

7

Hydrostatic Forces on Completely Submerged Plane Surfaces

Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

The magnitude of the

resultant force acting on a

plane surface of a completely

submerged plate in a

homogeneous (constant

density) fluid is equal to the

product of the pressure PC at

the centroid of the surface

and the area A of the surface.

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Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

To balance the bending-

moment portion of the

stress, the resultant

force FR does not act

through the centroid.

So, To find the

coordinates (xP, yP)

Hydrostatic Forces on Completely Submerged Plane Surfaces

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Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Hydrostatic Forces on Completely Submerged Plane Surfaces

The vertical location of the line of action is determined by equating the

moment of the resultant force to the moment of the distributed

pressure force about the x-axis:

or

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Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Hydrostatic Forces on Completely Submerged Plane Surfaces

Fortunately, the second moments of area about two parallel axes are

related to each other by the parallel axis theorem, which in this case is

expressed as:

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Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Hydrostatic Forces on Completely Submerged Plane Surfaces

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Ex1: Hydrostatic Forces on Completely Submerged Plane Surfaces

Solved Examples

The gate in the following figure is 5 ft

wide, is hinged at point B, and rests

against a smooth wall at point A.

Compute (a) the force on the gate due

to seawater pressure, (b) the

horizontal force P exerted by the wall

at point A, and (c) the reactions at the

hinge B.

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

13

Solved Examples

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Ex1: Hydrostatic Forces on Completely Submerged Plane Surfaces

14

Solved Examples

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Ex1: Hydrostatic Forces on Completely Submerged Plane Surfaces

15

Solved Examples

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Ex1: Hydrostatic Forces on Completely Submerged Plane Surfaces

16

Solved Examples

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Ex1: Hydrostatic Forces on Completely Submerged Plane Surfaces

17

Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Hydrostatic Forces on Completely Submerged Curved Surfaces

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Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Hydrostatic Forces on Completely Submerged Curved Surfaces

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Fluid statics

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.

Hydrostatic Forces on Completely Submerged Curved Surfaces

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Ex2: Hydrostatic Forces on Completely Submerged Curved Surfaces

Solved Examples

A long solid cylinder of radius 0.8 m

hinged at point A is used as an

automatic gate, as shown in the

following figure. When the water level

reaches 5 m, the gate opens by

turning about the hinge at point A.

Determine (a) the hydrostatic force

acting on the cylinder and its line of

action when the gate opens and (b) the

weight of the cylinder per m length of

the cylinder.

Lecture (3) – Fluid Mechanics I – 1st

year – Mechanical Dept.