Hydronamics

Hydronamics Points : hydronamics, bernoulli’s equation and its application, dynamics of fluid, energy of a liquid in motion, total head of a liquid particles in motion, bernoulli equation, limitations of bernoulli equation, practical application of bernoulli’s equation, Short Questions and Answers hydronamics Bernoulli’s Equation and its Application In the previous chapter, we have discussed the motion of liquid particles without taking into consideration any force or energy causing the flow. But in this chapter, we shall discuss me motion of liquids and the forces causing the flow. This topic is on known as Hydrodynamics. Dynamics of Fluid The dynamic of fluid flow is defined as that branch of science which deals with the study of fluids in motion considering of force which causes the flow. Energy of a Liquid in Motion The energy, in general, may be defined as the capacity to do work. Though the energy exists in many forms, yet the following are important from the subject point of view:
1 .Potential energy,
2.Kinetic energy, and
3.Pressure energy. Total Head of a Liquid Particles In Motion The total head of a liquid particle, in motion, is the sum of its potential head, kinetic head and pressure head. Mathematically, total head, Bernoulli Equation It states,’ For a perfect incompressible liquid, flowing in a continuous stream, the total energy of a particle remains the same, while the particle moves from one point to another.” This statement is based on the assumption that there are no “losses due to friction in the pipe. Mathematically,

Z+v²/2g + p/w = Constant
Z = Potential energy
v²/2g kinetic energy and
y²/2g = Presser energy Limitations of Bernoulli Equation The Bernoulli’s theorem or Bernoulli’s equation has been derived on certain assumption which are rarely possible. Thus the Bernoulli’s theorem has the following limitations:

1. The Bernoulli’s equation has been derived under the assumption that the velocity of every liquid particle, across any cross-section of a pipe, is uniform. But, in actual practice, it is not so. The velocity of liquid particle in the centre of pipe is maximum and gradually decreases towards the walls of the pipe due to the pipe friction. Thus, while using the Bernoulli’s equation, only the mean velocity of the liquid should be taken into account.

2. The Bernoulli’s equation has been derived under the assumption that no external force, except the gravity force, is acting on the liquid. But, in actual practice, it is not so. There are always some external forces (such as pipe friction etc.) acting on the liquid, which effect the flow of the liquid. Thus, while using the Bernoulli’s equation, all such external forces should be neglected. But, if some energy is supplied to, or, extracted from the flow, the same should also be taken into account.

3. The Bernoulli’s equation has been derived, under the assumption that there is no loss of energy of the liquid particle while flowing. But, in actual practice, it is rarely so. In a turbulent flow, some kinetic energy is converted into heat energy. And in a viscous flow, some energy is lost due to shear forces. Thus, while using Bernoulli’s equation, all such losses should be neglected.

4. If the liquid is flowing in a curved path, the energy due to centrifugal force should also be taken into account. Practical Application of Bernoulli’s Equation The Bernoulli’s theorem or Bernoulli’s equation is the basic equation which has the widest applications in Hydraulics and Applied Hydraulics. Since this equation is applied for the derivation of many formulae, therefore its clear understanding is very essential. Though the Bernoulli’s equation has a number of practical applications, yet in this chapter we shall discuss its applications on the following hydraulic devices:
1. Venturimeter 2. Orificemeter 3. Pitot tube. Short Questions and Answers Q.1: What is hydrodynamics? Ans: The motion of liquid particles without taking into consideration any force or energy is called hydrodynamics. Q.2: Write down the name of energy of a liquid In motion. Ans: (1) Potential energy (2) Kinetic energy (3) Pressure energy Q.3: Define the term of kinetic energy of a liquid particle in motion. Ans: If a liquid particle is flowing with a mean velocity of v meters per second, then the kinetic energy of the particle will be v²/2mg per kg of the liquid. Q.4: What is meant by the venturimeter? Ans: A venturimeter is an apparatus for finding out the discharge of a liquid flowing in a pipe. Q.7: Write down the name of venturimeter parts. Ans: (1) converging cone (2) throat (3) Diverging cone Q.8: Define the term orifice? Ans: An orifice meter is used to measure the discharge in a pipe. An orifice meter in its simplest form, consist of a plate having a sharp edge circular pole known as an orific. Q.9: Define the instrument of pitot tube. Ans: A pitot tube is an instrument to determine the e1ocity of flow at the required point in a pipe or a stream. Q.10: A pilot tube was entreated in a pipe to measure the velocity of water In it. If the water rises the tube is 200 mm find the velocity of the water.