## Example

An example will help illustrate one use of velocity head. A compressor is being considered for reuse in another application, and the question was raised as to the size of the inlet nozzle. The original conditions are stated as follows:

Inlet nozzle size: 18 inches Inlet flow: 10,000 CFM Inlet pressure: 25 psia Inlet temperature: 80°F Molecular weight: 29 Specific heat ratio: 1.35

The new conditions:

Inlet flow: 11,000 CFM Inlet pressure: 31 psia Inlet temperature: 40°F Molecular weight: 31 Specific heat ratio: 1.30

Description

K-Factor

Reducer contraction

0.50 0.3 Reducer enlargement

0.25 0.9 Gate valve

Fully open 0.15

0.25 open 25.0 Elbow

Miter 1.10

Close return bend 0.5

Swing check or ball valve 2.2

Angle valve, open 3.0

Globe valve, open 5.0 Filters

Clean 4.0

Foul 20.0

Intercoolers 17.0

Gas separators 7.0 Surge bottles

No choke tube 4.0

With choke tube 12.0

Casing inlet nozzle 0.5

Sidestream inlet nozzle (diaphragm) 1.0

Sidestream inlet nozzle (stage space) 0.8

Casing discharge nozzle 0.5

Extraction nozzle 0.8

Source: Modified from [16J.

By consultation with the original equipment maker, it has been determined that the vendor used a value of .2 velocity heads in the original design. From this information, K = .2. The effect of the rerate conditions on the inlet will be

233.7 x 60

Calculate the sonic velocity using Equation 2.32

where

R. = 1545/29 = 53.3 T = 80 + 460 = 540°F a = v 135Tx533~x322xS40 a = 1118.3 fps

Using Equation 2.33, calculate the Mach number

102.7

1118.3

This is a low value, therefore, the possibility exists of an up-rate relative to any nozzle flow limits. At this point, a comment or two is in order. There is a rule of thumb that sets inlet nozzle velocity limit at approximately 100 fps. But because the gases used in the examples have relatively high acoustic velocities, they will help illustrate how this limit may be extended. Regardless of the method being used to extend the velocity, a value of 150 fps should be considered maximum. When the sonic velocity of a gas is relatively low, the method used in this example may dictate a velocity for the inlet nozzle of less than 100 fps. The pressure drop due to velocity head loss of the original design is calculated as follows:

_ 53.3x540 V" 25x144

64.4 x 144

This is also a low value, so the proposed rerate conditions will be:

11,000x144

233.7x60

113 fps

49.8 x 500

31x144

5.58

The up-rate looks feasible considering that none of the inlet nozzle guidelines have been exceeded, the Mach number is still a low value, and the pressure drop is not significant. If the pressure drop had been significant, the effect of the drop could have been evaluated with respect to the compressor head and possibly a usable compromise worked out.

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