Question

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

Answer 1

The pressure drop in the pipe is approximately 181.2 N/m².

Step-by-step explanation:

The pressure drop in a pipe can be calculated using the Hagen-Poiseuille equation:

ΔP = (8ηLv) / (πr4)

Where ΔP is the pressure drop, η is the viscosity of the fluid (1.5 N.s/m² for glycerin), L is the length of the pipe (25 cm), v is the average velocity of the fluid (1.2 m/s), and r is the radius of the pipe (5.0 mm).

Substituting the given values into the equation:

ΔP = (8 * 1.5 * 0.25 * 1.2) / (π * 0.0054)

Simplifying the equation gives: ΔP ≈ 181.2 N/m²

Therefore, the pressure drop over the length of the pipe is approximately 181.2 N/m².

Answer 2

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

Step-by-step 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.