This equation is based on laws of conservation of energy. At the time of applying equation few assumptions are taken as follows
1. Fluid is steady and irrotational
2. Fluid is ideal ( non-viscous)
3. Fluid is incompressible
Bernoulli’s equation can b obtained by Euler’s equation as follows
As during deriving Bernoulli’s equation, we assumed that fluid is incompressible i.e. ρ = constant
Where head is energy / weight.
In real life, no fluid is ideal fluid and Real fluid are viscous in nature and hence will offer resistance to the flow. Bernoulli’s equation can be modified for real fluids by taking the head loss into account.
Applications of Bernoulli’s Equation
Venturimeter: With the help of this instrument rate of flow of fluid is measured through the pipe.
By applying Bernoulli’s equation between point 1 & 2, we get
If in equation, we use the differential U-tube manometer to give the value of h, then it is given by
where x is the difference of heavier column in U-tube
Hg is liquid filled in manometric tube
L is the liquid flowing inside venturimeter
Pitot Tube: With the help of this instrument the velocity of flow at any point in pope or channel can be measured.
It consists of a glass tube bent at a right angle.
It works on the principle that: If velocity of flow at any point becomes zero, then the pressure is increased at that point because kinetic energy converts into pressure energy.
Now applying Bernoulli’s equation between points 1 & 2.