FM 1

  • Terminal Velocity

1.Terminal velocity if a flow is due to a gravitational field

2. Terminal velocity if the flow is due to centrifugal motion

3. When stoke’s law is valid, i.e. Re <<1, for spherical particle terminal velocity due to gravitational field is given by

when flow due to centrifugal motion, terminal velocity under stoke’s law is given by

Note: At low Reynolds number, i.e., creeping flow, the drag coefficient is given by

For two identically sized particles, a ratio of terminal velocities is given by

In case of terminal velocity in stoke’s region (according to Stoke’s law), a calculation to be done as follows

  • Flow equation for Orifice meter

Velocity at vena contracta of orifice meter

Coefficient of contraction for orifice meter

  • Weber Number

Useful in analyzing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces

  • Velocity equation for laminar boundary layer

Where a1 and a2 are constants and y is the distance from the surface

  • Pitot tube

  • Ergun Equation for pressure drop due to flow across a porous packed bed

It includes energy loss due to viscous force characteristic of laminar flow and energy loss at high Reynolds number due to turbulence

  • Pressure drop for fluidization to start or pressure drop at the beginning of fluidization

  • Power number in case of turbulent flow

1.Power number in case of turbulent flow

2. Power number in case of laminar flow

  • Settling velocity of the suspension

Where n = Richardson – Zaki index

  • Kozeny – Carman equation

Kozeny – Carman equation for a pressure drop of fluid flowing across a packed bed of solids. Conditions for Kozeny-Carman equation is ԑ < 0.5, Re < 10.

The pressure drop across the fluidized bed for creeping flow(Re <1)

  • Burke-Plumer equation

For Re > 1000, Burke-Plumer equation is applicable for calculating pressure drop cross fluidized/porous bed.

  • Flow equation for rotameter

A metering ratio of a rotameter

For rotameter flow, Q is directly proportional to x, a height of the weight lifted due to flow.

  • One – seventh power law

Power law for relationships between wind speeds at one height and those at another. A one-seventh power law is for irrotational flow.

  • Hagen – Poisuille equation

For a flow of fluid in a cylindrical pipe of radius R, Hagen Poisuille equation is derived from equation

Velocity of fluid element as a function of radius r is given by

Pressure drop in fluid flowing through a cylindrical pipe of length l and diameter d; i.e., Hagen-Poiseuilli’s equation for laminar flows

  • Bingham plastic equation

Stress equation for Bingham plastic is given by

  • Head loss for energy losses due to bend, sudden expansion or
    contraction

  • Blasius equation for flat plate

1.Laminar flow

2. Turbulent flow

  • Friction factor

It is the ratio of shear force to inertial force.

1. A pressure drop across a cylindrical pipe (using fanning friction factor)

For laminar flow

2.Darcy friction factor(f) and fanning friction factor(ff)

A relationship between fanning friction factor and Darcy friction factor Fanning friction factor is one-fourth of Darcy friction factor