Continuity and bernoullis equation

The continuity equation is important for describing the movement of fluids as they pass from a tube of greater diameter to one of smaller diameter. It is critical to keep in mind that the fluid has to be of constant density as well as being incompressible. The Bernoulli equation is an important expression relating pressure, height and velocity of a fluid at one point along its flow. The relationship between these fluid conditions along a streamline always equal the same constant along that streamline in an idealized system.

1. Aldel Education Trust’s ST. JOHN COLLEGE OF ENGINEERING AND MANAGEMENT, PALGHAR (ST. JOHN POLYTECHNIC) D EPARTMENT OF MECHANICAL ENGINEERING S UB: FLUID MECHANICS AND MACHINERY T OPIC: CONTINUITY EQUATION & BERNOULLI’S EQUATION PREPARED BY:- Prof. Pranit Mehata Lecturer, SJCEM 7972064172

2. CONTINUITY EQUATION The continuity equation is based on the principle of conservation of mass It states as follows: “ If no fluid is added or removed from the pipe in any length then the mass passing across different sections shall be same.”

3. CONTINUITY EQUATION Let, = Area of the pipe at section 1–1, = Velocity of the fluid at section 1–1, = Density of the fluid at section 1–1 ,   are corresponding values at sections 2–2.   The total quantity of fluid passing through section 1–1= The total quantity of fluid passing through section 2–2 =     For incompressible fluids , =     Continuity Equation

4. DISCHARGE OR RATE OF FLOW It is defined as, “the quantity of a liquid flowing per second through a section of pipe or channel”. It is generally denoted by ‘ Q ’ Let A= cross sectional area of pipe and V= average velocity of fluid. Discharge Q is given by The SI unit of discharge is 1 OR    

5. DIFFERENT TYPES OF HEADS (ENERGIES) OF A LIQUID There are three types of energies or heads of flowing liquids Potential head or potential energy: Energy possessed by a fluid particle by virtue of its position from certain datum. It is denoted by Velocity head or kinetic energy: This is due to velocity of flowing liquid. It is measured as , V is the velocity of flow and ‘ g ’ is the acceleration due to gravity Pressure head or pressure energy: This is due to the pressure of liquid. It is given as , p is the pressure, and w is the specific weight of the liquid .   Total head/energy: Total head of a liquid particle in motion is the sum of its pressure head, kinetic head and potential head. It is measured in m of liquid    

6. ASSUMPTIONS MADE IN BERNOULLI’S EQUATION The fluid is ideal i.e. viscosity is zero The flow is steady and continuous The flow is incompressible The flow is irrotational The flow is one-dimensional

7. BERNOULLI’S EQUATION Bernoulli’s equation states as follows: “ In an ideal incompressible fluid when the flow is steady and continuous, the sum of pressure energy, kinetic energy and potential ( or datum ) energy is constant when particle moves from one point to another” Mathematically, =Constant Where, Z=Potential Head = Kinetic Head = Pressure Head  

8. BERNOULLI’S EQUATION By Bernoulli’s theorem, Total energy at section 1 = Total energy at Section 2   Modified Bernoulli’s equation ,