Ethyl alcohol flows through a horizontal tube having a diame

Ethyl alcohol flows through a horizontal tube having a diameter of 10 mm. If the mean velocity is 0.15 m/s, what is the pressure drop per unit length along the tube? What is the velocity at a distance of 2 mm from the tube axis?

Solution

a) The pressure lose in the pipe is given by,

H_L = F x L/D x V² / 2g (head loss over the length L)

H_L = F x L / 10x 10^-3 x 0.15 / 2 x 9.81 = 0.0764 FL

where V - mean velocity, F - frictional factor , L/d - length to diameter ratio, g - gravitational acceleration

The head loss per unit length H_L / L, H_L (per unit length) 0.0764F.

b) The velocity at 2mm from the tube axis, i.e D = 2mm

Using the eqn, H_L = F x L/D x V² / 2g and solve for H_L at D = 2mm

H_L = F x L/2 x 10 ^-3 x V² / 2 x 9.81

V² = H_L x 2 x 2 x 10^-3 x 9.81 / FL Since H_L per unit length is found to be 0.0764 FL

V² = 0.0764 x 2 x 2 x 10^-3 x 9.81 = 0.003

V = sqrt 0.003 = 0.05 m / s