Hydrokinematics

Hydrokinematics Points : Hydrokinematics, Types of flow of the liquids (Hydro kinematics), Rate of Discharge, Types of flow of the liquids (Hydro kinematics): The subject of hydro kinematics deals with the study of velocity and acceleration of the liquid particles without taking into consideration any force or energy. Rate of Discharge The quantity of a liquid, flowing per second through a section of a pipe or a channel, is known as the rate of discharge or simply discharge. It is generally denoted by

Now consider a liquid flowing through a pipe
Let
a = Cross sectional area of the pipe, and
v = Average velocity of the liquid,
Discharge, Q = Area x Average velocity = a.v Notes: 1. If the at s in m² and velocity in m/s then the discharge,
Q = m² x m³/s = cumecs
2. Remember that I m 1000 liters.
Equation of continuity of a liquid flow
If an Incompressible liquid is continuously flowing through a pipe or a channel (whose cross-sectional area may or may not be constant) the quantity of liquid passing per second is the same at all sections. This is known as the equation of continuity of a liquid flow. It is the first and fundamental equation of flow.

Continuity of a liquid flow: Consider a tapering pipe through which some liquid is flowing. Types of Flow Lines In the last article. we have discussed that whenever a fluid is in motion, its innumerable particles move along certain lines depending upon the conditions of flow. Though there are many types of flow lines, yet the following are important from the subject point of view: Path Lines The path followed by a fluid particle in motion is called a path line. Thus the path line shows the direction of a .particle- for a certain period of time or between two given sections. Stream Lines The imaginary line, drawn in the fluid in such a way that the tangent to any point gives the direction of motion at the point, is called the stream line, Thus the stream line shows the direction of motion of a number of particles at the same time. An element of fluid, bonded by a number of streamlines, which confine the flow, is called stream tube. As there is no movement of fluid across a streamline, therefore no fluid can enter or leave the stream tube except at the ends. It is, thus, obvious that a stream tube behaves like a solid tube. Steak lines of filament lines The instantaneous pictures of the position of all fluid particles, which have passed through a given point at some previous time, are called streak lines or filament lines. For example, the line formed by smoke particles ejected from a nozzle is a streak line. Potential lines or Equipotential Lines We know that there is always a loss of head of the fluid particles, as we proceed along the flow lines. If we draw lines joining the points of equal potential on adjacent flow lines, we get potential lines or equipotential lines.

The lines AB. CD EF GH etc.. are streamlines and LM NO PO are potential lines as shown in fig

Types of Flows in a Pipe When a fluid is flowing in a pipe, the innumerable small particles get together and form a flowing stream. These particles, while moving, group themselves in a variety of waves e.g. they mar move m regular formation, just as disciplined soldiers do; or they may swirl jostle, like the individuals, in a disorderly mob. The type of flow of a liquid depends upon the manner ir which the particles unite and move. Though there are many types of the following are important from the subject point of view: Uniforms Flow A flow, in which the velocities of liquid per” at all sections of a pipe or channel are equal, is called a uniform flow. This term is generally applied to flow in channels Non-uniform flow A flow in which the velocity liquid particles at all sections of a pipe or channel are not equal, is called a non uniform blow. Streamline Flow A flow, in which each liquid particle has a definite path and the paths of individual particles do not cross each other, is called a streamline flow. It is also called a laminar flow. Turbulent Flow A flow, in which each liquid particle does not have a definite path, and the paths of individual particles also cross each other, is called a turbulent flow. Steady Flow A flow, in which the quantity of liquid flowing per second is constant, is called a steady flow. A steady flow may be uniform or non-uniform. Unsteady Flow A flow, in which the quantity of liquid flowing per second is not constant, is called unsteady flow.