Question

A stiff, 10-cm-long tube with an inner diameter of 3.5 mm is attached to a small hole in the side of a tall beaker. The tube sticks out horizontally. The beaker is filled with 20∘C water to a level 50 cmabove the hole, and it is continually topped off to it maintain that level.

What is the volume flow rate through the tube? The viscosity of water is 1.0×10−3Pa⋅s.

Answer 1

Presure difference across the tube is P = ρgh, where ρ is the density of water,

or, P = 4900 N/m²

viscosity of water is η = 1X10^-3Pa.s

radius of the tube r = 3.5mm/2 = 1.75X10^-3m

length of the tube is l = 10cm = 0.1m

volume flow rate is,

V/t = πPr⁴/8ηl = [(3.14)(4900 N/m²)(1.75X10^-3m)⁴]/8(1X10^-3Pa.s)(0.1 m)

or V/t = 1.8X10^-4 m³/s

So, the volume flow rate is 1.8X10^-4 m³/s

***************************************************************************************************
This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....