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)
DEPARTMENT OF MECHANICAL ENGINEERING
SUB: FLUID MECHANICS AND MACHINERY
TOPIC: 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, 𝐴1 = Area of the pipe at section 1–1,
𝑉1 = Velocity of the fluid at section 1–1,
𝜌1 = Density of the fluid at section 1–1,
𝐴2, 𝑉2 , 𝜌2are corresponding values at sections 2–2.
The total quantity of fluid passing through section 1–1=
𝝆𝟏𝑨𝟏𝑽𝟏
The total quantity of fluid passing through section 2–2 =
𝝆𝟐𝑨𝟐𝑽𝟐 𝝆𝟏𝑨𝟏𝑽𝟏 = 𝝆𝟐𝑨𝟐𝑽𝟐
For incompressible fluids, 𝝆𝟏= 𝝆𝟐
𝑨𝟏𝑽𝟏 = 𝑨𝟐𝑽𝟐
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 𝒎𝟑
𝑺
1𝒎𝟑 = 𝟏𝟎𝟎𝟎 𝒍𝒊𝒕𝒓𝒆𝒔 OR 𝟏𝒍𝒊𝒕 = 𝟏𝟎−𝟑𝒎𝟑
𝑸 = 𝑨 × 𝑽

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
𝒛.
Velocity head or kinetic energy: This is due to velocity of
flowing liquid. It is measured as
𝑽𝟐
𝟐𝒈
, 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
𝒘
, 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
𝑻𝒐𝒕𝒂𝒍 𝑯𝒆𝒂𝒅, 𝑯 =
𝒑
𝒘
+
𝑽𝟐
𝟐𝒈
+ 𝒛

6. ASSUMPTIONS
MADEIN
BERNOULLI’S
EQUATION
1. The fluid is ideal i.e. viscosity is
zero
2. The flow is steady and continuous
3. The flow is incompressible
4. The flow is irrotational
5. 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,
𝒑
𝒘
+
𝑽𝟐
𝟐𝒈
+ 𝒛=Constant
Where, Z=Potential Head
𝑉2
2𝑔
= Kinetic Head
𝑝
𝑤
= Pressure Head

8. BERNOULLI’S
EQUATION
By Bernoulli’s theorem,
Total energy at section 1 = Total energy at Section 2
𝑷𝟏
𝝆. 𝒈
+
𝑽𝟏
𝟐
𝟐𝒈
+ 𝒁𝟏 =
𝑷𝟐
𝝆. 𝒈
+
𝑽𝟐
𝟐
𝟐𝒈
+ 𝒁𝟐
Modified Bernoulli’s equation ,
𝑷𝟏
𝝆. 𝒈
+
𝑽𝟏
𝟐
𝟐𝒈
+ 𝒁𝟏 =
𝑷𝟐
𝝆. 𝒈
+
𝑽𝟐
𝟐
𝟐𝒈
+ 𝒁𝟐 + 𝒉𝑳