Bernoulli's Equation states that -
For an incompressible liquid (density constant) which is flowing inward a continuous stream; the full unloose energy remains the same for all the particles, when the particle is moving from ane betoken to unopen to other point.Mathematical aspect of Bernoulli's equation:
P1/w + (v2 )1/2g + z1 = P2/w +( v2)2 /2g + z1 = constant
Here
P1 , P2 = Pressure at points 1 in addition to ii
V1,V1 = velocity at points 1 in addition to ii
Z1 , Z2 = datum caput at points 1 in addition to 2
w= weight density of the liquid (also denoted yesteryear Greek alphabetic quality gamma)
Please read : A Complete Guide to Fluid Mechanics
Different types of energies or caput inward Bernoulli's equation
1. Potential unloose energy or potential head:
Potential unloose energy is the unloose energy stored inward a trunk because of changing its seat to a higher house the fixed datum head. It's denoted yesteryear Z.
2. Kinetic unloose energy or head:
It is due to the velocity of the fluid. It is denoted by v2 /2g. Here, v is the velocity in addition to g is the gravitational acceleration.
3. Pressure unloose energy or pressure level head:
This unloose energy is due to the pressure level of the liquid. It is denoted yesteryear P/w .
P has the unit of measurement Newton/square meter ,N/m2
W has the unit of measurement Newton / cubmic meter , N/m3 So,
Total Energy = Pressure unloose energy + Kinetic energy + Potential energy
Total Head = Pressure Head + Kinetic Head + Potential Head
Applications of Bernoulli's Equation:
1. Influenza A virus subtype H5N1 modified equation for the criterion of velocity inward a pitot subway scheme in addition to pitot static tin hold upward got from Bernoulli's equation.
2. The menstruation through venturi meter in addition to orifice meter tin hold upward measured yesteryear this equation.
3. Flow over notches in addition to weirs tin hold upward calculated.
Euler Equation or Bernoulli Differential Equation
Euler's equation is expressed as
dp/ρ + g.dx + v.dv = 0
Euler's Equation is based on unopen to assumptions:
1. Non-viscous flow.
2. Incompressible and homogeneous flow.
3. Steady flow.
4. Continuous flow.
5. Uniform velocity of the flow.
Please Read: