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Bernoulli’s Theorem

According to this theorem, the total energy, (pressure energy, potential energy and kinetic energy) per unit volume or mass of an incompressible and non-viscous fluid in steady flow through a pipe remains constant throughout the flow, provided there is no source or sink of the fluid along the length of the pipe (Fig. 8).
 
51225.png
Fig. 8
 
Mathematically, for unit volume of liquid flowing through a pipe.
51219.png constant
  • Bernoulli’s theorem for unit mass of liquid flowing through a pipe can also be written as:
     
    51213.png constant
  • Dividing above equation by g, we get
     
    51207.png = constant
Here P/ρg is called pressure head, h is called gravitational head, and v2 / 2g is called velocity head. From this equation Bernoulli’s theorem can be stated as: in streamline flow of an ideal liquid, the sum of pressure head, gravitational head, and velocity head of every cross section of the liquid is constant.




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