# Sizing example

Process engineer requested to design a system to load 50% sodium hydroxide into a carbon steel tank in his plant. Sodium hydroxide is considered a hazardous material, hence not recommended to move 50% sodium hydroxide at velocities over 6 ft/sec in carbon steel piping. The supply pump at the plant can generate a flow of up to 250 gpm. The recommended maximum pressure drop across the valves in the system is 3 psi. Specific gravity of the sodium hydroxide solution is 1.52. Please specify a control valve for this service.

Step 1: Find Cv

Fmax  =250 GPM
Gt      =1.52
ΔP     =3 psi

Cv value is 178

Step 2: Find literature of Cv value (at various opening of ball valve) versus Valve sizes.

Example below

 Size (NPT) Cv @10% Valve Opening Cv @25% VO Cv @50% VO Cv @75% VO Cv @100% VO 1″ 0,33 0,75 3 5 10 1-¼” 0,53 1,2 4,8 8 16 1-½” 0,83 1,88 7,5 12,5 25 2″ 1,33 3 12 20 40 2-½” 2,10 4,73 18,9 31,5 63 3″ 3,33 7,5 30 50 100 4″ 5,33 12 48 80 160 5″ 8,33 18,75 75 125 250 6″ 13,33 30 120 200 400

At 50% or more opening, in order to meet C178, then valve sizes should be 5″ or 6″ ball valve.

Step 3: Check piping minimum diameter.

What diameter pipe would correspond to a flow of 6 ft/sec?

A = πr² = π(d/2)²

v = 6 ft/sec

Fmax = 250 gpm = 0.557 ft³/sec

Since Fmax = Av = π(d/2)² · v

Then

A pipe with diameter larger than 4.1 inches shall not exceed the 6 ft/sec requirement.

Answer: Combination between step 3 and 2 is valve and piping size should be 5″ inch.