Question

At what speed the velocity head of water is equal to pressure head of 40 cm of mercury?

Answer 1

Pressure head of a fluid is nothing but the potential energy of fluid per unit volume and velocity head is the kinetic energy per unit volume.
Now potential energy = m (mass of fluid) x g(acceleration due to gravity) x h (height of fluid)
Mass = density x volume Hence,
Potential energy head = density x g x h
Similarly,
velocity head = 1/2 x density x velocity²
all the values used to be in S.I. units :-
Pressure head of mercury = density of mercury x g x 40/1000 joules/m³
velocity head of water = 1/2 x density of water x (velocityof water)²
On equating and putting g as 9.8 m/s² we get,
density of mercury x 9.8 x 40/1000 joules/m_³​ = 1/2 x density of water x (velocityof water)^2​
Hence, velocity of water = [( 2 x 9.8 x 40/1000 ) x (density of mercury/ density of water)]^1/2
velocity of water = 3.265 m/sec ( As the ratio of density of mercury and water is 13.6 )