# Upthrust and Viscosity

## Density

**Density**,**ρ**is defined as the mass per unit volume. It is measured in**Kgm**.^{-3}

**Density**: Mass per unit volume

## Upthrust

A fluid will exert a

**force upward**on a body if it is partly or wholly submerged within it. This is because the deeper into a fluid you go, the greater the weight of it and so the greater the pressure. This difference in pressure between the top and the bottom of the object produces an upward force on it. This is called**Upthrust**.According to

**Archimedes’ Principle**, the upthrust on an object in a fluid is equal to the**weight of the fluid displaced**. So the volume of the object multiplied by the density of the fluid.

**Upthrust = Weight of Fluid Displaced**

## Viscosity

In a fluid, each ‘layer’ experts a

**force of friction**of each other ‘layer’. This frictional force is also present when**solid object**moves through a liquid. This force is termed**Viscous Drag**. Viscous Drag is**greater in Turbulent Flow than Laminar Flow**.The size of the Viscous Drag in a fluid depends on the (coefficient of)

**Viscosity**of that fluid. Viscosity is given the letter**η**and is measured in**Kgm**or^{-2}s**Pa s**. The greater the Viscosity, the greater the Viscous Drag.In most

**liquids**,**Viscosity decreases as temperature increases**, whereas in most**gases**,**Viscosity increases as temperature increases**. It is therefore important to always measure the temperature of a fluid when measuring Viscosity.

- It is possible to calculate the drag force exerted on a spherical object in a fluid using
**Stoke’s Law**:

**F = 6πηrv**

**Stoke’s Law assumes Laminar Flow**, and so**low velocities**.In this equation,

represents**v****Terminal Velocity**. This means that the**forces acting on the object are balanced**. This means that is it possible to form an equation be equating**Weight with Upthrust and Viscous Drag**(or, in the case of Upward Motion, Upthrust with Weight and Viscous Drag).