Glycerin, with a viscosity of 1.5 N ∙ s/m 2, is flowing with an average speed of 1.2 m/s through a tube that has a radius of 5.0 mm and is 25 cm long. What is the drop in pressure over the length of this pipe

The pressure drop over the length of the pipe is 140000 kPa.

Explanation:

let R be the radius of the pipe.

let V be the volume flow rate.

let v be the average speed of the Glycerin.

let A be the area of the pipe.

then, the volume flow rate is given by:

V = v*A

V = [π*P*r^4]/[8*Vi*L]

[π*P*r^4]/[8*Vi*L] = v*A

P = [8*Vi*L]*v*A/[π*r^4]

= [8*Vi*L*v*π*r^2]/[π*r^4]

= [8*Vi*L*v]/[r^2]

= [8*1.5 * (25*10^-2) * (1.2) ]/[ (5*10^-2) ^2]

= 140000 kPa

Therefore, the pressure drop over the length of the pipe is 140000 kPa.