Simple Manometers: Piezometer

Simple Manometers
A simple manometer is one which consists of a glass tube, whose one end is connected to a point where pressure is to be measured and the other end is open to atmosphere.

Piezometer
Piezometer is one of the simplest forms of manometers. It can be used for measuring moderate pressures of liquids. The setup of piezometer consists of a glass tube, inserted in the wall of a vessel or of a pipe. The tube extends vertically upward to such a height that liquid can freely rise in it without overflowing. The pressure at any point in the liquid is indicated by the height of the liquid in the tube above that point.



Pressure at point A can be computed by measuring the height to which the liquid rises in the glass tube. The pressure at point A is given by p = wh, where w is the specific weight of the liquid

Limitations of Piezometer
1. Piezometers can measure gauge pressures only. It is not suitable for measuring negative pressures.

2. Piezometers cannot be employed when large pressures in the lighter liquids are to be measured since this would require very long tubes, which cannot be handled conveniently.

3. Gas pressures cannot be measured with piezometers, because a gas forms no free surface.

Manometers

What are Manometers?
Manometers are devices used for measuring the pressure at a point in a fluid, by balancing the column of fluid by the same or another column of fluid.

Types of Manometers
Manometers are classified as:

1. Simple manometers


• Piezometer


• U-tube manometer, and


• Single column manometer


• Vertical single column manometer


• Inclined single column manometer


2. Differential manometers


• U-tube differential manometer


• Inverted U-tube differential manometer

Advantages of Manometers

• Easy to fabricate and relatively inexpensive
  
• Good accuracy
• High Sensitivity
• Requires little maintenance
• Suitable for low pressure and low differential pressure

Flow Net

What is a Flow Net?
A grid obtained by drawing a series of stream lines and equipotential lines is known as a flow net.

Equi-Potential Line is an imaginary line in a field of flow such that the total head is the same for all points on the line, and therefore the direction of flow is perpendicular to the line at all points.

Path line and Stream line

Distinguish between stream line and path line
1. A stream line is an imaginary line drawn in a flow field such that a tangent drawn at any point on this line represents the direction of the velocity vector. Path line is the line traced by a single fluid particle as it moves over a period of time.

2. Stream line shows the direction of velocity of a number of fluid particles at the same instant of time. Path line shows the direction of velocity of the same fluid particle at successive instants of time.

Can the path line and a streamline cross each other at right angles?
A fluid particle always moves tangent to the streamline. In steady flow, the path lines and streamlines are identical. In unsteady flow, a fluid particle follows one stream line at one instant and another at the next instant and so on, so that the path line have no resemblance to any given instantaneous streamline.

Stream Line and Velocity Potential

Define Stream line
A stream line is an imaginary line drawn in a flow field such that a tangent drawn at any point on this line represents the direction of the velocity vector.

In steady flow, a fluid particle will move along a streamline.

Equation of a stream line in a three-dimensional flow is given as
(dx/u) = (dy/v) = (dz/w)

Define Velocity Potential
Velocity Potential is defined as a scalar function of space and time such that its negative derivative with respect to any direction gives the fluid velocity in that direction.

Properties of a velocity potential function
1. If velocity potential exists, the flow should be irrotational
2. If velocity potential satisfies the Laplace equation, it represents the possible steady, incompressible, irrotational flow.