1

Pervious Lecture Contents 2

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

1. Characteristics of Pressure

2. Pressure of fluid at rest

3. Measurement of Pressure

Simple manometers

Differential manometers

Mechanical gauge

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

3

4

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

Hydrostatic Forces on Plane Surfaces

Fluid statics

A

a

A

a

A

dAhApdAhppdAF sinhfrom Figure

x

y

5

Fluid statics

Hydrostatic forces on plane surfaces

By definition A

CG dAA

1

sinsin CGa

A

a AApdAApF

CGCG h sin

ApAhpAhApF CGCGaCGa

To balance the bending-moment portion of the stress, the resultant force F does not act through the centroid. So, To find the coordinates (xCP, yCP)

x

y

CP

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

6

Fluid statics

Hydrostatic forces on plane surfaces

To compute yCP

x

y

CP

yCP

AA

a

A

cp dAydApyypdAyF sinsin

yCG

xx

AA

CGcp IdAyydAyF sinsin 2

where 0A

ydA

and Ixx is the area moment of inertia of the plate

area about its centroidal x axis

Ap

Iy

CG

xxCP sin

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

7

Fluid statics

Hydrostatic forces on plane surfaces

To compute xCP

x

yCP

yCP

xy

AA

CGa

A

cp IdAxydAypxdAxpxF sinsinsin where Ixy is the product of inertia of the plate

For positive Ixy, xCP is negative because the dominant pressure force acts in the third or lower left, quadrant of the panel. If Ixy= 0, usually implying symmetry, xCP = 0 and the center of pressure lies directly below the centroid on the y axis.

If ambient pressure pa is neglected pCG =γhCG

Ap

Ix

CG

xy

CP sin

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

8

Fluid statics

Hydrostatic forces on plane surfaces

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

9

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

Example 1: Hydrostatic forces on 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.

10

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

Example 1: Hydrostatic forces on plane surfaces

Solved Examples

11

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

Example 1: Hydrostatic forces on plane surfaces

Solved Examples

12

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

Example 1: Hydrostatic forces on plane surfaces

Solved Examples

13

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

Example 1: Hydrostatic forces on plane surfaces

Solved Examples

14

Fluid statics

Force to pressure vessels

Cylindrical pressure vessel

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

15

Fluid statics

Force to pressure vessels

Cylindrical pressure vessel

the stress σ1 is called circumferential stressor the hoop stress, and the stress σ2 is called the longitudinal stress or the axial stress.

σ2

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

16

Fluid statics

Force to pressure vessels

Cylindrical pressure vessel

lrplt 22 1 t

pr

21

Equilibrium of forces to find the

circumferential stress:

Equilibrium of forces to find the

longitudinal stress

prrt 2

22 t

pr2

σ2

12 2

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

17

Fluid statics

Spherical pressure vessel

Force to pressure vessels

2prF

trm 2forceHorizontal

2

trrm

22 rptrm

t

rp

2

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

18

Fluid statics

Buoyancy and Stability

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

19

Fluid statics

Pressure Distribution in Rigid-Body Motion

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

20

Fluid statics

Pressure Distribution in Rigid-Body Motion

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

21

Example 2: Pressure Distribution in Rigid-Body Motion

Solved Examples

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

The coffee cup in the following figure is removed from the drag racer, placed on a turntable, and rotated about its central axis until a rigid-body mode occurs. Find (a) the angular velocity which will cause the coffee to just reach the lip of the cup and (b) the gage pressure at point A for this condition.

22

Example 2: Pressure Distribution in Rigid-Body Motion

Solved Examples

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

23

Example 2: Pressure Distribution in Rigid-Body Motion

Solved Examples

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

24

Quiz

Homework

25

Find the net hydrostatic

force per unit width on

the rectangular gate AB

in the following figure

and its line of action.

Lecture (3) – Mechanical Engineering (2) – 2nd year – Electrical Power Dept.

26

27

Exam (1) on 04/11/2015

28