Question

A volume of 7.3 m3 of glycerol (η = 0.934 Pa·s) is pumped through a 11-m length of pipe in 51 minutes. The pressure at the input end of the pipe is 7.4x105 Pa, and that at the output end is atmospheric pressure. What is the pipe's radius?

Answer 1

Answer:

17.7 mm

Explanation:

Poiseuille's law can be used to solve for the radius of the pipe

Volume per seconds flowing through the pipe = 7.3 / (51 × 60 s) = 0.0239 m³ / s

volume per seconds = π R^4 ( Pi - Po) / ( 8 ηL) where R is the radius of the pipe in mm, (Pi - Po) is the pressure difference in Pa, L is the length of the pipe in meters, and η is the viscosity in Pa.s

Pi - Po = ( 7.4 - 1.01) × 10^5 since 1 atm represent atmospheric pressure and it is equal to 1.01 × 10^5

Pi -Po = 6.39 × 10^5

substitute the values into the equation

0.00239 = 3.142 × (R^4) × 6.39 × 10^5 / ( 8 × 11 × 0.934)

cross multiply

0.00239 × 8 × 11 × 0.934 = (R^4) × ( 2.01 × 10^6)

make R subject of the formula

R^4 = (0.00239 × 8 × 11 × 0.934) / ( 2.01 × 10^6)

R = $\fourthroot{9.77 * 10^-8}$  

R = 0.0177 m = 17.7 mm