Calculation Problems

Three types of problems arise:

• Sizing Problem

• Flow Calculation Problem

• DP Calculation Problem

Sizing Problem

This is the normal design function given a flow rate and a differential pressure; calculate the b factor of the flow element that will satisfy the conditions.

Because often the designer wants a full scale differential pressure corresponding to a round figure, it pays to allow a full scale flow rate and full scale DP to specified as well as specifying a normal flow. In this case the first step is to calculate the normal differential pressure.

If the designer enters a full scale flow rate and full scale DP without specifying a normal flow rate, then a normal flow rate of the full scale flow rate is applied as a reasonable estimate of what the expected normal flow will be.

Then using this value for the normal differential pressure and the normal flow, the design proceeds by iteration until sufficient precision is achieved:

1. First, assume C = 0.6, e = 1.0.

2. Step 1, calculate b using Equation 1.

3. Step 2, using the calculated b, calculate C.

4. Step 3, using b, calculate e (in the case of compressible fluid only).

5. Go back to step 1 and continue looping until convergence is achieved.

Once b has been calculated, the actual maximum flow at the full scale differential pressure is back calculated and displayed (this shows the difference between the nominal maximum flow originally specified and the actual maximum flow). Similarly if a minimum flow had been nominated, then the DP at the minimum flow is also calculated.

Note: The b calculation is always done for normal flow.

Flow Calculation Problem

This situation arises when an orifice is in use (so b is known) and a differential pressure reading exists and someone needs to know what the flow is.

Normally the data is simply entered in the normal flow column and the calculation is carried out. If the normal flow conditions are not filled in, the system tries to guess the normal conditions from the data given.

The calculation proceeds as follows:

6. First, assume C = 0.6, e = 1.0.

7. Step 1, calculate the flow.

8. Step 2, calculate the Reynolds number.

9. Step 3, calculate C.

10. Step 4, calculate e.

11. Return to step 1 and iterate until convergence is achieved.

DP Calculation Problem

This calculation is required if an existing flow element is in service but an increase in throughput is required. New full scale and normal flows are usually nominated and the transmitter needs to be re-ranged. b is known.

If only the full scale flow rate is given, then the normal flow is assumed as the maximum flow rate.

The calculation proceeds as follows:

12. Since the flow and b are known, the Reynolds number and C are calculated. Assume e = 1.0.

13. Step 1, the differential pressure is calculated with pdrop.

14. Step 2, e is calculated (only necessary for compressible fluids).

15. Return to step 1 and iterate until convergence is achieved.

The calculation is carried out for all the flows nominated.