Washington UniversityChE 433 Digital Process Control Laboratory

FluidStatics & Dynamics

Lecture

Fluid StaticsProperties

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, centipoiseDerived from Newton's Equation of Viscosity

= - (dV/dy)

Various Fluids

Fluid Temp DegF

Weight Density lb/ft^3 Sp Gr

Viscosity Cp

Water 100 61.99 0.993 0.7SAE 10 Lube 60 54.64 0.876 100Benzene 100 54.8 0.878 0.66Therminol FR1 100 85.1 1.364 28

Pressure Units

P = F/A, Force / Areapsia = pounds/in^2 absolute 1Atm = 14.7 psia

psig = pounds/in^2 gauge or psi above atmosphericExample: 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 psig

@ 60 DegF

1 foot H20 Head = 0.4337 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

1 A tm osphere

P ressureincreases

linearly

P=Height*Density

What about 10 feet deep in Lake Superior?

Methanol Tank

10 feet

Patm = 14.7 psia

M ethanolW t D ensity49.1 lb /ft^3

Bottom Pressure = ?psig

Our Lab Level Measurements useD/P, differential pressure

D /P T ransm itter

G as

differential pressure

The differenceThe bottom pressure minus the top pressure.

ThenIf we know the fluid density, we know the level.

Be careful of the density change vs. temperature

Fluid Dynamics

Fluid Dynamic FundamentalsFlow = Velocity*Area

Reynolds Number; Dimensionless

<2000 laminar, >4000 turbulent, transition between

VAQ

Dv

Re

Flow Profiles

At very low velocities of high viscosities, RD 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 fluidEnergy is ft-lbs but the pounds are factored out of each term

Potential & Kinetic EnergiesSee the units cancel

P/lbs/ft^2 / lbs/ft^3 = feet

v^2/2g = (ft/sec)^2 / 2 * ft/sec^2 = feetBut what about hl?

lhg

vPZ

g

vPZ

22

222

2

211

1

hl = 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

g

v

D

Lf

g

Kvhl 22

22

VAQ

g

QKhl 2

21

hl = head loss due to flow

And hl is directly proportional to the pressure:

Valve Cv The water flow rate, GPM, that would result in a 1.0 psid pressure drop across it.

lhP

1

P

GQ

PQCv

)4.62(

What about our lab?

14

inches

Patm = 14.7 psia

1.5 feet d ia

BottomPressure = ?

W ater

0.5 G P M

0.5 G P M

What is the Cv 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 aself 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

% open Cv5 0.009

10 0.01420 0.0330 0.0640 0.1150 0.1760 0.2570 0.3580 0.4590 0.60

100 1.00

Extra lab/homework assignment:

Let's see if we can calculate the Cv of FV1-1 flowing at 0.5 GPM?