Measuring liquid flow using pressure sensors

Differential pressure sensors are widely used to measure the flow rate of incompressible liquids such as water. The most common method is to measure the pressure drop across an orifice plate in a pipeline and calculate the flow rate. An orifice plate is simply a plate installed in the pipeline, usually between flanges, with a central orifice of known size. When fluid flows through the orifice, a pressure drop is generated across the orifice from the upstream to the downstream side. This pressure drop is proportional to the flow rate, and the sensor signal can be used to calculate the flow rate in engineering units.
The figure shows a typical orifice plate configuration. The upstream side of the orifice plate has a higher pressure and is connected to the "+" port of the pressure sensor via a three-valve manifold. The downstream side of the orifice plate is similarly connected to the "-" port of the pressure sensor. The three-valve manifold protects the pressure sensor from overpressure when installed in the working pipeline.
The calculation method for calculating flow rate from pressure drop is based on a relatively simple physical equation. However, many variables are involved in the calculation, each with its own engineering units. These variables include orifice geometry, pipe size, fluid viscosity, and fluid density. The calculation can be quite complex due to the number of terms and conversion factors involved in each variable. Fortunately, there are many online calculators available that allow you to calculate flow rate for a given orifice pressure drop by simply entering variables in any convenient engineering units.
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The example you provided details how to use the relationship between the differential pressure sensor signal (Vdc or mA) and the orifice pressure drop to derive flow rate, and establishes the corresponding conversion formula. This method is a typical application of differential pressure flow measurement.
The core of your content is correct, and the process is clear. The following is a summary and minor optimization based on your calculation process and industry knowledge (such as the Q∝ΔP relationship mentioned in the search results), mainly concerning the rigor of the formula expression.
Calculation Process Summary
Your calculation logic is correct. The following is a summary of the key steps:
1. Confirm the relationship between flow rate and differential pressure:
2. Flow rate (Q) is proportional to the square root of the differential pressure (ΔP), that is, Q=kΔP
3. Your data sheet confirms this:
4.
- When ΔP = 100 in H₂O, Q = 640 GPM
- When ΔP = 25 in H₂O, Q ≈ 320 GPM (theoretical calculation) / 321 GPM (actual table)
5. Calculate the orifice coefficient (k):
6. Calculate using the formula k = Q / ΔP.
- Take the first row of data: k = 640 / 100 = 640 / 10 = 64
- Optimization suggestion: More rigorously write the formula as k = Q / ΔP. Your original text omitted the variable sign for k = GPM / √(ΔP).
7. Verify the orifice plate coefficient (k):
8. Calculate another data point using k=64 to verify its general applicability:
- Calculation: Q = 64 × 25 = 64 × 5 = 320 GPM
- Comparison: In your table, Q = 321 GPM when ΔP = 25 in H₂O.
- Analysis and Optimization: There is a slight difference of 1 GPM between the calculated value (320 GPM) and the table value (321 GPM). This confirms your reference to "approximately 1% accuracy" and "1-2 GPM difference," which are acceptable in engineering applications. If you seek extremely high accuracy, you should verify the original data or coefficients.
9. Derive the flow rate formula based on the sensor signal type:
- For a Vdc signal (0-5V):
- Voltage and differential pressure are linearly related: ΔP = (100 in H₂O/5V) × Vdc = 20 × Vdc. - The flow rate formula is: Q = kΔP = 64 × 20 × Vdc
- You calculated k′ ​​= 286.217 using k′ = Q / Vdc, so Q = 286.217 × Vdc. This formula is correct; essentially, Q = 64 × 20 Vdc = 64 × 20 × Vdc ≈ 286.217 × Vdc.
- For a mA signal (4-20 mA):
- The differential pressure is linearly related to the effective current: ΔP = [100 In H₂O / (20 − 4) mA] × (ImA − 4) = 6.25 × (ImA − 4).
- The flow rate formula is: Q = kΔP = 64 × 6.25 × (ImA − 4) = 64 × 2.5 × (ImA − 4) = 160 × (ImA − 4).
- You calculated k′′ = Q / ImA − 4 to obtain k′′ = 160, so Q = 160 × (ImA − 4). This formula is correct.
- Verification: Q = 160 × (8 − 4) = 160 × 2 = 320 GPM. The discrepancy from the 321 GPM in the table again reflects the possible slight errors in the system.
Things to Consider:
Some practical considerations apply. The three-valve manifold must be used with an orifice plate and a differential pressure sensor. This allows the pressure sensor to be used while the pipeline is pressurized. To do this, connect the positive and negative ports of the pressure sensor to closed isolation valves while simultaneously opening the equalizing valve. Then, slowly open the isolation valves to evenly distribute the static pressure in the pipeline across both sides of the pressure sensor. The opening of the equalizing valve eliminates any possibility of a high differential pressure being applied to the sensor. Once the pressure sensor is fully connected, the equalizing valve closes, allowing the pressure sensor to sense the pressure differential across the orifice plate.
To decommission the pressure sensor, first open the equalizing valves and then close the isolation valves. When the isolation valve is fully closed, any residual pressure in the sensor cavity will vent through the pressure sensor vent port. The equalizing valve can then be closed to disconnect the pressure sensor from the manifold. Please note that all operations must be performed in this exact order: when placing the pressure sensor into service, open the equalizing valve first; when removing the pressure sensor from service, close the equalizing valve last.
Material compatibility is another consideration. 316 SS wetted parts are the best choice for pressure sensors measuring water flow. Validyne also offers Inconel wetted parts for more corrosive fluids. The O-ring material in the pressure sensor body must also be compatible with the fluid; Validyne offers a variety of elastomer compounds.
For pipes with an inner diameter greater than 2 inches, orifice plate flow measurement is considered the most accurate. The orifice plate must be located within a straight pipe run, away from elbows or tees. The pipe leading to the orifice plate should maintain a straight run length that is several times the pipe diameter. The gaskets in the orifice plate flange must be carefully aligned and not impede fluid flow within the pipe, otherwise measurement errors may occur. There are other flow measurement technologies available, including vane meters, turbine meters, electromagnetic flow meters, and others. Orifice plates and differential pressure sensor systems continue to be used because they are low cost, low maintenance, and provide reasonably accurate measurements across a wide range of pipe sizes, liquid types, and flow rates.