Formulas Used For Liquids

Base Sizing Formula

It is given by equation 2 in section 4.1 of the standard:

Where w is the mass flow rate, r is the density, P1 and P2 are the pressures respectively upstream and downstream. N6 is a unit correction factor and FP is the piping factor (see Section Effects of Fittings below).

Reynolds Number Formula

Eq. 11 section 4.4

Where q is the volumetric flow rate, d is the nominal body size, FL is the valve recovery coefficient and n is the kinematic viscosity. Since our design is based on mass flow rate and the absolute viscosity is more often used. The formula has been modified to the following one, equivalent but not published in the standard.

Here we use w (kg/hr) instead of q (m3/hr) and the absolute viscosity, m, in mPa.s (centipoise). The 1000 factor is the base density of water. N4 is the coefficient corresponding to q in m3/hr i.e. N4 = 76000. Fd is a valve factor (for all practical purposes if a valve internal has a single flow path, Fd = 1, if it has multiple flow paths, Fd = sqrt(n). In general valves have either 1 or 2 paths and Fd is either 1 or 0.7).

Effects of Fittings

The effect of reducers and expanders before and after the valve is described in the standard under section 4.3. The base piping factor FP is given by the following formula:

Eq. 3 Section 4.3

And Eq. 4 Section 4.3

The factors with subscript 1 are due to the inlet fitting; the factors with subscript 2 are due to the outlet fitting. The fitting formulas assume the pipe is larger or equal than the valve size. The formulas are nonsensical when a valve larger than the line is used. Since all corrections are approximate only, it is satisfactory to use nominal sizes here instead of actual sizes.

Where D1 is the inlet pipe diameter and d is the valve body size.

Where D2 is the outlet pipe diameter and d is the valve body size.

The KB factors are not loss factors but represent the conversion of pressure to kinetic energy, or vice versa, within the fittings. They are called the Bernoulli factors and are expressed as:

When the inlet and outlet pipes are the same size, they cancel out.

Choking

When P1 and P2 are defined, inside the valve there exists a section where the pressure is at a minimum. This pressure is called PVC where 'VC' stands for 'Vena Contracta'.

The factor FL is obtained experimentally by the valve manufacturer. It is defined as:

If the downstream pressure is lowered sufficiently, at a certain value the vena contracta pressure reaches the vapour pressure of the liquid and the liquid starts to boil. At this stage, lowering the downstream pressure further does not produce an increase in flow rate, the vena contracta pressure remaining at the boiling point of the liquid. The valve is said to be choked.

There are 2 modes of choking depending on whether the downstream pressure is less or greater than the vapour pressure. If the downstream pressure is less than the vapour pressure, the flow remains two phase all the way to the valve exit, the valve is said to be flashing. If the downstream pressure is greater than the vapour pressure of the liquid, the valve is said to be cavitating. Both flashing and cavitation produce a lot of noise but of the two, cavitation is far more severe as the vapour bubbles created at the vena contracta implode nearer the exit and cause a lot of erosion on the metal parts. Valves left cavitating can literally destroy themselves in minutes.

One thing to notice during choking is that the flow is solely determined by the pressure difference between inlet and the vena contracta, and it follows that the outlet fittings no longer have any significance on the flow rate.

The flow formula becomes:

Where Equation G1 and PV is the vapour pressure and PC is the critical pressure.

FLP is a factor which combines the recovery factor and the piping geometry and we use Equation 16 to calculate it:

Eq 16 section 5.3

The fitting(s) function returns the following values:

For liquids it also returns FF and FLP.