P=p/a
The direction of this pressure is always at right angles to the surface, with which the fluid at rest, comes in contact Pressure Heads Consider a vessel containing some liquid as shown in We know that the liquid will exert pressure on all sides as well as bottom of the vessel. Now let a bottomless cylinder be made to stand in the liquid as shown in the figure.
Let
W = specific weight of the liquid,
H = Height of liquid in the cylinder, and
A = Area of the cylinder base.
A little consideration will show, that there will be some pressure on the cylinder base due to weight of the liquid in it. Therefore pressure,
A little consideration will show, that there will be some pressure on the cylinder base due to weight of the liquid in it. Therefore pressure,
P = Weight of liquid in the cylinder/ Area of the cylinder base
whA/A= wh
This equation shows that the intensity of pressure at any point, in a liquid is proportional to its depth, from the surface (as w is constant for the given liquid). It is thus obvious, that the pressure can be expressed in either of the following two ways.
1. As a force per unit area i.e., N/m, kN/m etc.
2. As a height of the equivalent liquid column.
The intensity of pressure in brief, is generally termed as pressure.
Note: The pressure is always expressed in pascal (briefly written as Pa) such that 1 Pa = 1N/m, 1kPa = 1
KN/m2 1 MPa = 1 MN/m2 = 1N/mra2 Example Find the pressure at a point 4 m below the free surface of water:
Solution:
Given:
h = 4m.
We know that pressure at the point,
p = wh = 9.81 x 4 39.24 KN/m2 = 39.24 kPa Ans. Atmospheric Pressure It has been established, since long, that the air possesses some weight, Subsequently, it was also thought that the air, due to its weight, must exert some pressure on the surface of the earth. Since the tar Is compressible, therefore its density is different at different heights. The density of air has also been found to vary Prom time to time due to the changes in its temperature and humidity. It is thus obvious, mat due to these difficulties, the atmospheric pressure (which is due to weight of the atmosphere or air above the surface of the earth) cannot be calculated, as is done in the case of Liquids. However, it Is measured by the height of the column of liquid that it can support.
It has been observed that at sea level, the pressure exerted by the column of air of 1 square metre cross- sectional area and of height equal to that of the atmosphere is 103 kN. Thus we may say that the atmospheric pressure at the sea level is 103 kN/m2 (or 103 kPa). It can also be expressed as 10.3 metres of water, in terms of equivalent water column or 760 mm of mercury in terms of equivalent mercury column. Gauge Pressure It is the pressure, measured with the help of a pressure measuring instrument, in which the atmospheric pressure is taken as datum. Or in other words, the atmospheric pressure on the gauge scale is marked as zero. Generally, this pressure is above the atmospheric pressure. Absolute Pressure It is the pressure equal to the algebraic sum of atmospheric and gauge pressures. It may be noted that if the gauge pressure is minus (as in the case of vacums or suctions). the absolute pressure will be atmospheric pressure minus gauge pressure, e.g., if the absolute pressure at any point is 150 kN/m and the atmospheric pressure is 103 kNm2. then the gauge pressure at that point will be 150- 103 =47 kN/m. A little consideration will show, that if the pressure intensity at a point is more than the local atmospheric pressure, the difference of these two pressures is called the positive gauge pressure. However, if the pressure intensity is less than the local atmospheric pressure, the difference of these two pressures is called the negative gauge pressure or vacuum pressure.
Mathematically.
Pabsolute + Pghauge Plezometer Tube A plezometer tube is the simplest form of instrument, used for measuring, moderate pressures. It consists of a tube, one end of which is connected to the pipeline in which the pressure is required to be found out. The other end is open to the atmosphere, in which the liquid can rise freely without overflow. The height, to which the liquid rises up in the tube, gives the pressure head directly.
If the pressure of a liquid flowing in a pipe is to be found out, the piezometer tube is connected to the pipe as shown in Fig. While connecting the piezometer to a pipe, care should always be taken that the tube should not project inside the pipe beyond its surface. All burrs and roughness near the hole must be removed, and the edge of the hole should be rounded off. It may e noted that plezometer tube is meant for measuring gauge pressure only as the surface of the liquid, in the tube, is exposed to the atmosphere. A piezometer tube is also not suitable for measuring negative pressure; as in such a case the air will enter in the pipe through the tube. Manometer Strictly speaking, a manometer is an improved form of a piezometer tube. With the help of a manometer, we can measure comparatively high pressures and negative pressures also. Following are the few types of manometers:
1. Simple manometer
2. Micromanometer
3. Differential manometer, and
4. Inverted differential manometer. Simple Manometer A simple manometer is a slightly improved form of a piezometer tube for measuring high as well as negative pressures. A simple manometer, in its simplest form consists of a tube bent in U-shape, one end of which is attached to the gauge point and the other is open to the atmosphere as shown in Fig.
The liquid used in the iu rIbt or simple manometer is, generally, mercury which Is 13.6 times heavier than water Hence it is suitable for measuring high pressures also.
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