# Flowrate to Differential Pressure (DP) Calculator

**Flow Transmitter Differential Pressure Calculator**

For the purpose of calculating the differential pressure of the flow transmitter with a known flow rate, the following calculator was utilized.

The relationship between flow and differential pressure in a flow element, such as an orifice plate or a venturi tube, is typically a square root relationship. This means that the flow rate (Q) is proportional to the square root of the differential pressure (ΔP). The formula to calculate the flow rate from differential pressure is:

Where:

- ( Q ) is the flow rate.
- ( C ) is a constant that incorporates the characteristics of the flow element and the fluid properties.
- (ΔP) is the differential pressure.

When we have a linear relationship between the flow rate and the output current of a transmitter (4-20 mA), the differential pressure is related to the square of the flow rate. Therefore, to find the DP at a certain flow rate, we need to square the ratio of the flow rate to the maximum flow rate and then multiply by the maximum DP.

**Formula for Linear mA (I mA):**

The linear mA is the current that corresponds linearly with the flow. The formula is:

** Formula for Square Root mA (Sq.I mA): **

The square root mA is the current that corresponds to the square root of the flow. The formula is:

**Formula for Differential Pressure (DP): **

The DP can be found using the square root relationship between flow and DP. The formula is:

The formula to calculate DP based on the square root relationship with PV flow, accounting for a non-zero DP Low, is:

**Example Calculation: Determining Differential Pressure (DP) from Known Flow Rate (PV)**

Let’s step through an example calculation using the provided data:

Given Parameters:

- I High = 20 mA
- I Low = 4 mA

- PV High = 200 m³/hr
- PV Low = 0 m³/hr
- PV = 100 m³/hr (given flow)
- DP High = 500 mBar (at PV High = 200 m³/hr)
- DP Low = 0 mBar (at PV Low = 0 m³/hr)
- PV = 100 m³/hr (the flow rate for which we want to find the DP)

**Step 1: Linear Calculation of Current (mA)**

Let’s calculate I mA for PV = 100 m³/hr:

**Step 2: Square Root Calculation of Current (mA)**

Using the same values as above. Let’s calculate Sq.I mA for PV = 100 m³/hr

**Step 3: Differential Pressure Calculation**

**For zero based calculation**

So, the correct DP when the PV flow is 100 m³/hr is indeed 125 mBar. This calculation is based on the square root relationship between flow and differential pressure, which is a common principle in fluid dynamics and flow measurement

**For non zero based calculation**

This formula will give you the DP at a PV of 100 m³/hr, taking into account the non-zero DP Low value. You would replace X with the actual value of DP Low to get the specific result.

For example, if DP Low was 10 mBar, the calculation would be:

So, with a non-zero DP Low of 10 mBar, the DP when the PV flow is 100 m³/hr would be 132.5 mBar.

Please replace X with your actual DP Low value to perform the calculation for your specific scenario.