Question

Name the physical quantity corresponding to each term of Bernoulli equation

Answer 1

Bernoulli's equation can be viewed as a conservation of energy law for a flowing fluid. It is given as  

p1 + ρv1²/2  + ρgh1 = p2  +ρv2²/2  +ρgh2

Here p1, v1 and h1 are pressure, speed and height of the fluid in first phase.  

When the flud moves to different location, the pressure, speed and height are given by p2, v2 and h2.  

ρ is the fluid density.  

g - acceleration due to gravity

If you see clearly, ρv1^2/2 is the kinetic energy of the fluid in first position, ρgh1 is the potential energy of the fluid in the first position.  

So we are equating total energy in first state to second state.

Answer 2

Bernoulli equation is given by:-

P/ρ + 1/2v² + gz = C

P is the pressure, V is the velocity,  ρ is the density, z is the distance, g is the  acceleration due to gravity.

In this case, the dimensional variables are P, v, z.

Dimension constant are -  g , ρ, C, 1/2

Each term in this

equation including the constant has dimension of [L² T⁻²].

Hence, this is dimensionally homogeneous.