Fluids & Flow

Fluid Level (m)
Fluid Velocity (m/s)
Volume flow rate (m^3/s)
Mass flow rate (kg/s)
Velocity distribution/profile
Viscosity (N.s/m^2)
Surface tension (N/m)

Types of Fluids & Flow Measurements

weight of a volume of fluid
hydrostatic pressure based on depth in a liquid
buoyancy forces that change position of a float
resistance or conductance between terminals
dielectric constant in a capacitor
ultrasonic reflection off a surface

Common Principles of Fluid Level Measurement

assume:
steady flow
flow along a streamline
inviscid flow
incompressible flow

Bernoulli equation

common device for quantifying fluid velocity based on stagnation pressure

pitot-static tube

pitot-static tube equation

measure fluid velocity based on effectiveness of heat transfer away from a heated wire
- output is voltage that is needed to balance a bridge circuit
- major advantage: directional sensitivity 3-axis probes to acquire u/v/w velocity components
- use a thin film rather than a wire for less sensitive to contamination for variant of the same principle of hot-wire anemometer

Hot-wire Anemometer

uses interference patterns between beams to establish a "grid" of light and dark fringes
- when particle pass through the fringe patter they scatter light
- a photodetector and signal processing algorithms extract the time-varying light intensity to determine the velocity of the particle
- very small particles are dominated by viscosity therefore move with the same velocity as the surrounding fluid
- common to "seed" the fluid with particles of preferred size and concentration

Laser-doppler velocimeter (LDV)

a common device for quantifying flow rate Q based on differences in pressure P
- flow nozzles and orifice meters follow similar principles and are less expensive but suffer greater energy losses

Venturi Meters

Venturi Meter Pressure equation

use drag on floating object in equilibrium with its weight and buoyancy to indicate volume flowrate by position of the float
- float geometry and channel profile can be customized for a wide variety of liquids and gases
- most rotameters are used only for measurement by visual inspection

Rotameters

Various Mechanical Displacement Flowmeters

diverts a portion of the flow into a sensing tube, and uses temperature sensors to measure how effectively the fluid is heated

Thermal mass flowmeter

q: rate of heat transfer
cp: specific heat
m_dot: mass flow rate
T: temperature

Deliberate rate of heat transfer q

the result of an imbalance of cohesive molecular forces between interior molecules and those at the surface
- force equilibrium dictates that surface tension σ times
the perimeter of a spherical droplet with radius R must balance the
differential pressure ∆p times the mid-section area
- force equilibrium also reveals that the force of surface tension 2πRσ,
balancing the weight of a liquid column, determines the height h of that
column
- 1-micron capillary can support a water column 30m

Surface Tension