Flow & resistance of fluid in a tube

1) Laminar Flow via a tube

• Movement of a given amount of fluid in a specified time between two points
• For this movement to occur, must be a pressure difference between the two points [pressure gradient]
• Source of pressure differential that causes flow may be gravity or motion imparted by a pump

Algebraic rearrangement:

OR Poiseuille’s Law

Law of fluid flow:

DP: pressure difference or gradient

r: radius of tube

L: length of tube

V: viscosity of the fluid

8: constant of proportionality

• For a given tube, the fluid volume flow rate increases linearly with the applied pressure
• The longer the tube and the more viscous the fluid, the less the flow
• The wider the tube the more flow it will carry

2)Turbulent Flow via a tube

• Under turbulent flow conditions, Poiseuille’s Law no longer applies
• Reynolds number is a dimensionless quantity whose magnitude gives an indication of whether flow is laminar or turbulent

Re = [mean velocity x density x diameter]¸ Viscosity

• Re < 2000: flow is likely to be laminal
• Re > 2500: flow is likely to be turbulent

• For a channel of a given size and shape, there is, for any given fluid (viscosity), an upper limit of flow to which the fluid motion proceeds as if in layers constituting laminal flow. Beyond such limits the flow is turbulent, and the lateral motions include eddies and swirling paths

3) Flow through a Orifice

• In contrast to laminar flow through a tube which is dependent on the viscosity of the gas flowing, flow through an orifice,(which may be considered to be a special form of a tube whose radius is much greater than its length) depends on the square root of the density of the gas, as well as the area of the orifice and the square root of the applied pressure. It is, however, relatively independent of viscosity