### F3viii / 18A13: Viscocity Density Gas Flow

## 18A13: Exam Report

### Explain the difference between viscosity and density (10% of marks). Describe the effects of changes in viscosity and density on the flow of gases and liquids (90% of marks).

**46% of candidates passed this question.**

Whilst most candidates defined density correctly, there was a lot of uncertainty regarding viscosity. Most candidates recognised that flow may be laminar, turbulent or transitional. Most accurately recounted Reynolds number and applied this correctly. Additionally, the Poiseuille equation was correctly stated by most candidates and correctly related to laminar flow. Few candidates recalled the equation describing turbulent flow.

## Definitions

- Behaviour of a gas in flow depends on 2 intrinsic properties of the gas

**DENSITY**= the ratio of mass to volume**VISCOSITY**= internal property of fluid*(gas/liquid)*which is a measure of resistance to flow

## Flow

**Flow**= the volume of fluid*(gas/liquid)*passing a point in unit time

### Turbulent Flow

- Disorganised air flow moving in the same direction
- More likely at high flow rates
**Density dependent***( viscosity independent**)*- Described by Fanning Equation

- It is
**less efficient**because ∆P varies directly with V^{2} - ∴for a given flow, the necessary driving P is greater
- The driving P is proportional to the square root of the flow rate, the density of the gas and inversely proportional 5
^{th}power of the tube radius

### Transitional Flow

- Flow neither fully turbulent or fully laminar
- There is a gradual transition from laminar → turbulent

### Reynold’s Number

- A dimensionless number used to determine if flow is going to be laminar or turbulent

- Low (<2000) = laminar flow because viscous forces predominante

= smooth, consistent fluid motion

- High (>2000) = turbulent flow

= random eddies, vortices, flow fluctuations

= dominated by inertial forces

### Helium

- He is a colourless, odourless, non-toxic element
- 2
^{nd}most abundant element in the universe, but rare on earth - Much less dense cf. O
_{2}

## Gas

## Density (g/L)

## Viscosity (Poise)

He

0.179

201.8

O_{2}

1.429

211.4

- ∴↓resistance to air flow
- Because will give you lower Re & more likely to give laminar air flow
- ∴Helium can be used in diseases of ↑airway R
*e. asthma, infant airway obstruction*

- Author: Krisoula Zahariou