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THE RELATIONSHIP BETWEEN THE PV FLOWRATE AND THE PV PRESSURE (A REVIEW)

The Process Technology and Operator Academy Posted on by

I'd be nothing', nothing', nothing', nothing'Nothing', nothing', nothing', nothing'Nothing', nothing', nothing', nothing' without you

("Nothing Without You," sung by The Weeknd, 2016)

 

A REVIEW OF THE RELATIONSHIP BETWEEN THE PV FLOWRATE AND A CHANGE IN THE PV PRESSURE

No ΔP=No Flow.

Brilliant PTOA Readers and Students ... meaning those who are reading the PTOA Segments in the intended, sequential order ... already know the Universe has mandated that the PV Flowrate shall be totally dependent upon the PV Pressure. The "Transport Phenomena" which govern the flow of fluids, heat, and electrons were previously featured in PTOA Segment #158.

To be more accurate:

The PV Flowrate owes its existence to a change in the PV Pressure.  

The height of the liquid column in each cylinder correlates to the PV Pressure exerted by the flowing liquid in the pipe. The change in liquid height correlates to the decreasing PV Pressure sensed between P1 and P2 and P3. PTOA Readers and Students already know how to convert a change in liquid height into a ΔP with units of psi.

The "Change in PV Pressure" has many nicknames:

  • Delta P
  • ΔP
  • dP
  • Pressure Drop 
  • Pressure Gradient

 

No matter what the change in PV Pressure is called:

The PV Flowrate cannot exist if there is no driving force provided by a change in the PV Pressure ... AKA  ΔP.

No ΔP=No Flow.

 

This graph shows that as the Pressure Drop on the Y-Axis increases, the Flowrate of a Coolant measured in gallons per minute (gpm) increases on the X-Axis. Note that when the Pressure Drop=0 there is no measurable flowrate.

 

This Outside Process Operator is recording local Temperatures, Pressures, Levels and Flowrates.

Brilliant PTOA Readers and Students have already tested their understanding of the PV Flowrate-Δ PV Pressure Relationship:

In PTOA Segment #158 PTOA Readers and Students were challenged to deduce the status of a pipeline which had two Pressure Indicators (PIs) located 200 feet apart, both reading the same line pressure of 150 psi. Answer:

The pipe was liquid full yet the liquid inside the pipe was not flowing.

PTOA Readers and Students also learned that when a fluid is flowing through a pipe, the upstream PI will read a greater magnitude of the PV Pressure than the downstream PI.

Tell me why, Fred!

Because ...

The direction of the Flowrate is always from the area of High Pressure of the ΔP to the area of Low Pressure of the ΔP.

 

More ΔP= More Flowrate .... Less ΔP= Less Flowrate

The upward change of ΔP on the Y-Axis reflects a proportional change in Flowrate (Q) on the X-Axis which has the magnitude Q times Q ... which is Q2.

The previous paragraphs predict the direction of a flowing fluid, but what about the magnitude of the flowing fluid?

The Universe has figured the magnitude of the PV Flowrate out, too.

The magnitude of the ΔP is proportional to the magnitude of the PV Flowrate!

 

 

THE UNIVERSE REVEALS HOW TO MEASURE THE PV (Volumetric) FLOWRATE

To recap ... the Universe revealed to Humankind that:

  • ΔP causes a fluid to flow and
  • The magnitude of the ΔP is directly related to the magnitude of the PV Flowrate.

 

Humankind used this information to design instruments which can detect and measure the PV Flowrate.

PV Flowrate detection and measurement devices which use an upstream higher-Pressure sensing tap and a downstream lower-Pressure sensing tap to measure ΔP ... and hence infer a PV Flowrate from that ΔP ... are "(liquid) head measuring instruments."

Installing an upstream "higher PV Pressure tap" and a downstream "lower PV Pressure tap" made it possible to calculate a ΔP. When the PV Flowrate changed, so did the observed ΔP.

PTOA Readers and Students will soon learn the form and function of popular PV Flowrate devices used for the detection and measurement of the PV Flowrate.  For now, PTOA Readers and Students just need to know that when two PV Pressure taps are used to determine a ΔP and hence infer a PV Flowrate, the PV Flowrate device is a "(Liquid) Head-Measuring" instrument.

To be more accurate:

When the PV Flowrate is inferred from a Head Instrument ... the PV Flowrate will be proportional to the SQUARE ROOT OF ΔP.

Oops! Fred is a wee bit confused!

The Relationship between ΔP (DP) and Flowrate mandated by the Universe is on the left-hand side of the graphic. Taking the Square Root of both ΔP (DP) and Flow2 reveals the directly linear relationship between the PV Flowrate and the Square Root of ΔP (DP) shown on the right hand side of the graphic.

Fred...

the left side of the nearby graphic illustrates how the Universe mandates fluids shall flow.

Pretend the magnitude for FLOW (X-Axis) indicates values for what is actually "FLOW Squared" aka FLOW2.

Conceptualizing the PV Flowrate in terms of Flow2 is hard for all of Humankind to comprehend, not just for Fred.

Once upon a time, PV Flowrates were recorded on logarithmic paper so that Humankind did not have to do the math and take the square root of the measured and detected Flowrate.

Once upon a time back in the day of slide rulers and before the microchip existed ... PV Flowrates were recorded on logarithmic paper which was one way "to extract the square root" but made it really hard to clearly read the lower-end magnitudes of the PV Flowrate.

Nowadays "Smart Transmitters" do the math and the result is shown on the right-hand side of the graphic. A directly linear relationship between the square root of the ΔP (DP) and the PV Flowrate results when "the square root is extracted."

Always remember and never forget that The Universe decreed Transport Phenomena like the relationship between the PV Flowrate and ΔP.  Humankind just observed what was going on and developed a definition/mathematical relationship between the two factors that seemed to explain repeated observations of the laws mandated by the Universe.

In the process of interpreting the laws of the Universe regarding fluid flow, Humankind figured out that:

  • Humankind observed the laws of the Universe and figured out that the PV Flowrate ("Q" on the left hand side) is equal to a Constant ("K) times the Square Root of ΔP.

    The most crucial factor that creates a PV Flowrate is the driving force provided by the ΔP.

  • To obtain an accurate PV Flowrate, a few more factors need to be taken into consideration.

 

The more complete definition/mathematical relationship between the PV Flowrate and the  ΔP PV Pressure is shown in the blue-shaded box nearby.  Note that the PV Flowrate is abbreviated "Q."  The letter "Q" is often used to abbreviate something that is flowing, be it heat or electrons or fluids.

The terms in the above expression are:

A restriction in gas flow is intentionally created by inserting an Orifice Plate into the interior of a pipe through which the gas flows. The ΔP that results (labelled PDT in the diagram) is sensed and measured by inserting an upstream High Pressure tap and a downstream Lower Pressure tap. The calculated ΔP is thence used to infer a Gas Flowrate. Note that the Gas Flowrate is corrected for flowing Temperature (the RTD and TT) and Flowing Pressure (the PT).

Q = a VOLUMETRIC FLOWRATE that in the real world is expressed with units like "cubic meters per hour" (M3/hr) or "gallons per hour" (gal/hr) or "cubic feet per hour" (ft3/hr) or "barrels per day" (Bbls/day), etc.

K = a Constant ...  basically a "fudge factor" ... which makes the units on both sides of the equation work out. However, "K" also takes into account fluid properties and features of the pipe that the fluid is flowing through.

ΔP = the difference in PV Pressure which is determined from calculating the difference between an upstream High-Pressure tap and a downstream Low-Pressure tap.

Nowadays, the actual PV Flowrate-ΔP PV Pressure relationship mandated by The Universe is easy to forget.

"Square root extraction" is no longer performed by humans. Ergo, nobody could fault Process Operators for thinking there is a directly linear relationship between the PV Flowrate and ΔP.

However, Instrumentation Technicians must never forget that the PV Flowrate is directly proportional to the SQUARE ROOT OF ΔP. Until AI takes over, the Instrument Tech shall be calibrating the head-type instruments that infer the magnitude of a PV Flowrate in terms that Humankind can easily understand.

 

QUICK REVIEW OF THE PV PRESSURE ↔ FLUID VELOCITY SWAP  

Volumetric Flowrate (Q) is equal to the Velocity of the flowing fluid (V) multiplied by the Cross-Sectional Area of the Pipe the fluid is flowing through (A).

In the recent PTOA Segment #235, PTOA Readers and Students learned that the two contributing factors of a Volumetric Flowrate are:

  • The fluid's Velocity and
  • The Cross-Sectional Area through which the fluid flows.

 

Brilliant PTOA Readers and Students are already aware that the Velocity Factor of a Volumetric Flowrate has a relationship with the PV Pressure. At this point in their PTOA journey, every PTOA Reader and Student could do a core competent presentation on the PV Pressure ↔ Fluid Velocity Swap that makes it possible to build up pressure energy in non-compressible fluids ... aka liquids:

  • The PV Pressure ↔ Fluid Velocity Swap is illustrated when fluid flows through this Venturi-shaped Pipe. The gas's Velocity and Pressure are midscale prior to entering the swaged-down pipe diameter. While approaching the shortest pipe diameter, the gas Velocity progressively increases while the gas's PV Pressure progressively decreases.  After flowing into an expanded pipe diameter with the same diameter as before, the gas's Velocity and PV Pressure swap back to very close to the midscale values that were observed as the fluid flowed into the Venturi-shaped pipe.

    The PV Pressure ↔ Fluid Velocity Swap was defined in PTOA Segment #159.

  • Application of the PV Pressure ↔ Fluid Velocity Swap in Centrifugal Pumps was featured in PTOA Segment #176.
  • The PV Pressure ↔ Fluid Velocity Swap was revealed to be the same as "The Venturi Effect" in PTOA Segment #207.
  • Application of The Venturi Effect in Hydraulic Lift Jet Pumps was featured in PTOA Segment #208.

 

Next up? the relationship of the PV Flowrate and the PV Temperature!

 

TAKE HOME MESSAGES: This PTOA Segment reviewed and clarified the important relationship between the PV Flowrate and the ΔPV Pressure.

The PV Flowrate is totally dependent upon a ΔP to exist. The greater the ΔP, the greater the PV Flowrate, and vice versa. The direction of flow is always from the higher-Pressure of the ΔP (aka "upstream") to the lower-Pressure of the ΔP. (aka "downstream").

The term Pressure Differential can also appear as:

  • Delta P
  • ΔP 
  • dp
  • Pressure Drop
  • Pressure Gradient

 

The PV Flowrate-ΔPV Pressure relationship is used in every (Liquid) Head Measuring Instrument.  In (Liquid) Head Measurement Instruments, the PV Flowrate is proportional to the SQUARE ROOT of the ΔP that provides the driving force for the PV Flowrate. Nowadays, the transmitters which transmit the PV Flowrate measurements as standard signals apply an algorithm called a "square root extractor" that linearizes the Flowrate reading into a one-to-one correspondence with the square root of ΔP.

The PV Pressure ↔ Fluid Velocity Swap relationship was reviewed in this PTOA Segment.  "Venturi-shaped PV Flowrate Instruments" illustrate the PV Pressure ↔ Fluid Velocity Swap relationship.

©2023 PTOA Segment 0241

PTOA PV FLOWRATE FOCUS STUDY AREA
THE RELATIONSHIP OF THE PV FLOWRATE WITH PV TEMPERATURE, PV PRESSURE, AND PV LEVEL

 

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