Washington University ChE 433 Digital Process Control Laboratory Fluid Statics & Dynamics Lecture

Fluid Statics Properties Liquids – Incompressible Fluids How heavy is it? - Weight Density, lbs/ft^ 3 Specific Gravity, G, is the Weight Density of Fluid / Weight Density of H2O How thick is it? - Viscosity, centipoise Derived from Newton's Equation of Viscosity  = -  (dV/dy)

Various Fluids

Pressure Units P = F/A, Force / Area psia = pounds/in^ 2 absolute 1Atm = 14.7 psia psig = pounds/in^ 2 gauge or psi above atmospheric Example: 50 psig = 64.7 psia psid = pounds/in^ 2 differential, i.e. A pressure drop or loss across anything in the pipe line i.e. A control valve. psi units are usually assumed to be psig. (See convert.exe on web site for other conversions.)

Other Useful Units Inches of water 27.67” H2O = 1 60 DegF 1 foot H20 Head = psig 1 ft^ 3 of water weighs 62.4 pounds 1 gallon of water weighs 8.33 pounds

Level Measurement Measure the pressure at the bottom of the tank. Pressure = height * density; inches*pounds/in^3 or pounds/in^2

P=Height*Density What about 10 feet deep in Lake Superior?

Methanol Tank

Our Lab Level Measurements use D/P, differential pressure

differential pressure The difference The bottom pressure minus the top pressure. Then If we know the fluid density, we know the level. Be careful of the density change vs. temperature

Fluid Dynamics Fluid Dynamic Fundamentals Flow = Velocity*Area Reynolds Number; Dimensionless 4000 turbulent, transition between

Flow Profiles

At very low velocities of high viscosities, R D is low and the fluid flows in smooth layers with the highest velocity at the center of the pipe and low velocities at the pipe wall where the viscous forces restrain it. This type of flow is called laminar flow and is represented by Reynolds numbers below 2,000. One significant characteristic of laminar flow is the parabolic shape of its velocity profile. At higher velocities or low viscosities the flow breaks up into turbulent eddies where the majority of flow through the pipe has the same average velocity. In the turbulent flow the fluid viscosity is less significant and the velocity profile takes on a much more uniform shape. Reynolds numbers above 4,000 represents turbulent flow. Between Reynolds number values of 2,000 and 4,000, the flow is said to be in transition.

Energy Equation for Fluid Flow, Bernoulli Energy is measured in feet of the fluid Energy is ft-lbs but the pounds are factored out of each term Potential & Kinetic Energies See the units cancel P/  lbs/ft^ 2 / lbs/ft^ 3 = feet v^ 2 /2g = (ft/sec)^ 2 / 2 * ft/sec^ 2 = feet But what about h l ?

h l = head loss due to flow Many experiments have shown head loss to be: K for pipe fitting; f L/D for pipe line K resistance coeff; f = friction factor; L = length in feet; D = dia in feet Remember that therefore

h l = head loss due to flow And h l is directly proportional to the pressure: Valve C v The water flow rate, GPM, that would result in a 1.0 psid pressure drop across it.

What about our lab?

What is the C v of the outlet manual valve? Ignore the fittings, etc

Potential Energy = Kinetic Energy The potential energy is the water head The kinetic energy is the loss across the valve If we doubled the flow, what would be the new level?

This is an example of a self regulated process. If we put the outlet valve at a fixed position, we would establish a level where the flow for the head pressure would balance the inlet flow.

Our lab inlet valve

Extra lab/homework assignment: Let's see if we can calculate the C v of FV1-1 flowing at 0.5 GPM?