What is

Fluid Pressure

?

 Fluid contained in a vessel exerts force on all its sides. The force per unit area is called Fluid Pressure.

 Mathematically-

p= P/A

where P= the force and A= area on which the force acts p= intensity of pressure S.I. unit is

N/m 2

or Pascal

Pressure Head-

 Represents the internal energy container. It may also be called of a fluid due to the pressure exerted on its static pressure head or simply static head .  Mathematically, h = p / γ where h =pressure head p =intensity of pressure γ =specific wt. of the liquid Hence, pressure intensity may be expressed in two ways 1.

2.

As force per unit area & As an equivalent static head.

Pascal’s Principle:

Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid.

A small force F 1 applied to a piston with a small area produces a much larger force F 2 on the larger piston. This allows a hydraulic jack to lift heavy objects.

Atmospheric,absolute and gauge pressure

Devices used for measuring pressure-

 Fluid pressure may be measured by following devices 1.

Manometers

(a) Simple manometers-

PIEZOMETER, U-TUBE MANOMETER & SINGLE COLUMN MANOMETER.

(b) Differential manometers-

U-TUBE DIFFERENTIAL MANOMETER & INVERTED U-TUBE DIFFERENTIAL MANOMETER. 2. Mechanical gauges BOURDON TUBE PRESSURE GAUGE, DIAPHRAGM PRESSURE GAUGE & VACUUM GAUGE.

MANOMETER measures pressure at a point in a fluid by balancing the column of fluid by the same or another column of fluid.

U-TUBE MANOMETER PIEZOMETER SINGLE-COLUMN MANOMETERS VERTICAL INCLINED

Differential manometers-

U-TUBE DIFFERENTIAL MANOMETER INVERTED U-TUBE DIFFERENTIAL MANOMETER

Simple manometers Consists of a glass-tube whose one end is connected to a point where pressure is to be measured and the other end is exposed to the atmosphere

Includes-

Piezometers U-tube manometers & Single-column manometers

PIEZOMETER

-

-

It is the simplest form of Manometer,used for measuring moderate pressure.It consist of a Tube,open at one end to the Atmosphere,in which,Liquid can rise freely without overflow,the Height,to which the Liquid rises up in the Tube,gives the Pressure Head directly.

p= γ h -

Measures gauge pressure only.

-

not suitable for measuring Negative Pressure because Air will enter in the pipe through the Tube Disadvantages Cannot be used for measuring large pressures in case of lighter liquids.

& Cannot be used for measuring gas pressures

U-tube manometer-

 "U"-Tube manometer enables the pressure of both

liquids

and

gases

to be measured with the same instrument.

S 2

 The fluid whose pressure is being measured should have a mass density less than that of the manometric fluid and the two fluids must be

immiscible

.

S 1

The pressures in the right limb and the left limb above the datum line B-C are equal

FOR POSITIVE GAUGE PRESSURE

Pressure head above B-C in the right limb= h 2 S 2 Pressure head above B-C in the left limb = h+h 1 S 1 Equating,

h+h 1 S 1 = h 2 S 2 OR, h= h 2 S 2 _ h 1 S 1

.

U-TUBE MANOMETER The pressures in the right limb and the left limb above the datum line X-X are equal Pressure head above X-X in the right limb= 0 Pressure head above X-X in the left limb = h+h 1 S 1 +h 2 S 2 Equating, h+h 1 S 1 +h 2 S 2 = 0 OR ,h =

_

( h 1 S 1 +h 2 S 2 )

FOR NEGATIVE GAUGE PRESSURE S 2

SINGLE COLUMN MANOMETER (VERTICAL)

S 1 Light liquid

A>>a

a= area of crossection A= area of crossection Datum line

A x Z 1 = a x h 2 Or, Z 1 = (a x h 2 )/A ............(1) Equating the pressure heads above the datum line Z-Z,

Heavy liquid S 2

h +(h 1 + Z 1 )S 1 = (h 2 + Z 1 )S 2 or, h = (h 2 + Z 1 )S 2 _ (h 1 + Z 1 )S 1 or, h = Z 1 (S 2 _ S 1 ) + h 2 S 2 = { (a x h 2 )/A } (S 2 _ h 1 S 1 _ S 1 ) + h 2 S 2 _ h 1 S 1 As A>>a, so ratio A/a is very very small and can be neglected and above equation becomes, h = h 2 S 2 _ h 1 S 1…………………………………………………… (2)

#useful for the measurement of small pressures and is more sensitive than the vertical tube.

-# Due to inclination the distance moved by the heavy liquid in the right limb is more.

Let, l = length of the heavy liquid moved in the right limb, θ = inclination of right limb horizontal and Z 2 = vertical rise of liquid in the right limb from X-X= l sin θ Putting the value of Z 2 in equation (2) we get,

h = l sinθ x S 2 _ h 1 S 1 SINGLE COLUMN MANOMETER (INCLINED)

Differential U-tube manometer-

 a differential manometer is used to measure the difference in pressures between two points in a pipe, or in two different pipes. -most commonly used types 1.U-tube differential manometer.

2.Inverted U-tube differential manometer

Case 1.Figure (a) below shows a differential manometer whose two ends are connected with two different points A and B at the same level and containing same liquid .

We know that the pressures in the left limb and the right limb , above the datum line X-X, are equal Pressure head in the left limb = h A Pressure head in the right limb = h B + (h +h 1 )S 1 + h 1 S 1 + hS Equating, h A + (h +h 1 )S 1 or, h A - h B = h B + h 1 = h ( S – S S i.e. difference of pressure head,

h A - h B = h ( S – S 1 )

1 ) 1 + hS

case 2- Figure (b) below shows a differential manometer whose two ends are connected with two different points A and B at different levels and containing different liquids.

We know that the pressures in the left limb and the right limb , above the datum line X-X, are equal Pressure head in the left limb = h A Pressure head in the right limb = h B + (h +h 1 )S 1 + h 2 S 2 + hS Equating, or, h A h A - h B + (h +h 1 )S 1 = h B + h 2 S 2 + hS = h ( S – S 1 ) + h 2 S 2 - h 1 S 1 Thus, difference of pressure at A and B,

h A - h B = h ( S – S 1 ) + h 2 S 2 - h 1 S 1

Mechanical gauges-

 Used for measuring

medium

and

high

pressures.

 Employs elastic systems such as tubes, diaphragms, bellows,etc.



Types

Bourdon tube pressure gauge.

Diaphragm gauge & Vacuum gauge.

Bourdon tube pressure gauge

The bourdon tube pressure instrument is one of the

oldest

pressure sensing instruments in use today. The bourdon tube consists of a thin-walled tube that is flattened diametrically on opposite sides to produce a cross-sectional area

elliptical

in shape, having

two long flat sides

and

two short round sides

. The tube is bent lengthwise into an arc of a circle of 270 to 300 degrees. Pressure applied to the inside of the tube causes

distension of the flat sections

and tends to restore its original round cross-section. This change in cross section causes the tube to

straighten slightly

.

BOURDON TUBE PRESSURE GAUGE

Since the tube is permanently fastened at one end,

the tip of the tube traces a curve

that is the result of the change in angular position with respect to the centre. Within limits, the movement of the tip of the tube can then be used to position a

pointer

to indicate the applied internal pressure.

Diaphragm gauge-



This type of gauge employs a metallic disc or diaphragm instead of a bent tube. This tube or diaphragm is used for actuating the indicating device.

Referring to the figure below, when pressure is applied on the lower side of the diaphragm it is deflected upward. This movement of the diaphragm is transmitted to a rack and pinion. The latter is attached to the spindle of needle moving on a graduated dial. The dial can again be graduated in a suitable scale.

Vacuum Gauge-

Bourdon gauges discussed earlier can be used to measure vacuum instead of pressure. Slight changes in the design are required for this purpose. Thus, in this case, the tub is bent inwards instead of outwards as in pressure gauges. Vacuum gauges are graduated in millimetres of mercury blow the atmospheric pressure. In such cases, therefore, absolute pressure in millimetres of mercury is the difference between barometer reading and vacuum gauge reading.

Vacuum gauges are used to measure the vacuum in the condensers, etc. if there is leakage the vacuum will drop.