mathematics

Souders–Brown equation

Souders–Brown equation is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Souders–Brown equation rather than just read about it. In short: In chemical engineering, the Souders–Brown equation (named after Mott Souders and George Granger Brown) has been a tool for obtaining the maximum allowable vapor velocity in vapor–liquid separation vessels (variously called flash drums, knockout drums, knockout pots, compressor suction drums and compressor inlet drums). It has also been used for the same purpose in designing trayed fractionating columns, trayed abso…

Key takeaways

Souders–Brown equation belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Souders–Brown equation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Souders–Brown equation from memory before moving on to harder problems.

Reference excerpt

In chemical engineering, the Souders–Brown equation (named after Mott Souders and George Granger Brown) has been a tool for obtaining the maximum allowable vapor velocity in vapor–liquid separation vessels (variously called flash drums, knockout drums, knockout pots, compressor suction drums and compressor inlet drums). It has also been used for the same purpose in designing trayed fractionating columns, trayed absorption columns and other vapor–liquid-contacting columns. A vapor–liquid separator drum is a vertical vessel into which a liquid and vapor mixture (or a flashing liquid) is fed and wherein the liquid is separated by gravity, falls to the bottom of the vessel, and is withdrawn. The vapor travels upward at a design velocity which minimizes the entrainment of any liquid droplets in the vapor as it exits the top of the vessel.

Use The diameter of a vapor–liquid separator drum is dictated by the expected volumetric flow rate of vapor and liquid from the drum. The following sizing methodology is based on the assumption that those flow rates are known. Use a vertical pressure vessel with a length–diameter ratio of about 3 to 4, and size the vessel to provide about 5 minutes of liquid inventory between the normal liquid level and the bottom of the vessel (with the normal liquid level being somewhat below the feed inlet). Calculate the maximum allowable vapor velocity in the vessel by using the Souders–Brown equation:

v = k ρ L − ρ V ρ V {\displaystyle v=k{\sqrt {\frac {\rho _{L}-\rho _{V}}{\rho _{V}}}}}

where

v is the maximum allowable vapor velocity in m/s ρL is the liquid density in kg/m3 ρV is the vapor density in kg/m3 k = 0.107 m/s (when the drum includes a de-entraining mesh pad) Then the cross-sectional area of the drum can be found from:

A = V ˙ v {\displaystyle A={\frac {\dot {V}}{v}}}

where

V ˙ {\displaystyle {\dot {V}}} is the vapor volumetric flow rate in m3/s A is the cross-sectional area of the drum And the drum diameter is:

D = 4 A π {\displaystyle D={\sqrt {\frac {4A}{\pi }}}}

The drum should have a vapor outlet at the top, liquid outlet at the bottom, and feed inlet at about the half-full level. At the vapor outlet, provide a de-entraining mesh pad within the drum such that the vapor must pass through that mesh before it can leave the drum. Depending upon how much liquid flow is expected, the liquid outlet line should probably have a liquid level control valve. As for the mechanical design of the drum (materials of construction, wall thickness, corrosion allowance, etc.) use the same criteria as for any pressure vessel.

Recommended values of k The GPSA Engineering Data Book recommends the following k values for vertical drums with horizontal mesh pads (at the denoted operating pressures):

At a gauge pressure of 0 bar: 0.107 m/s At a gauge pressure of 7 bar: 0.107 m/s At a gauge pressure of 21 bar: 0.101 m/s At a gauge pressure of 42 bar: 0.092 m/s At a gauge pressure of 63 bar: 0.083 m/s At a gauge pressure of 105 bar: 0.065 m/s GPSA notes:

k = 0.107 at a gauge pressure of 7 bar. Subtract 0.003 for every 7 bar above a gauge pressure of 7 bar. For glycol or amine solutions, multiply above k values by 0.6 – 0.8 Typically use one-half of the above k values for approximate sizing of vertical separators without mesh pads For compressor suction scrubbers and expander inlet separators, multiply k by 0.7 – 0.8

Illustrations

Souders–Brown equation: Typical vapor–liquid separator — Typical vapor–liquid separator

Worked examples

Example 1 — a first encounter with Souders–Brown equation

Start with the simplest possible case. Write down what Souders–Brown equation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Souders–Brown equation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Souders–Brown equation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Souders–Brown equation

In research: Souders–Brown equation appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Souders–Brown equation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Souders–Brown equation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Equations, Gas-liquid separation, so understanding it makes those chapters shorter.
In everyday life: Look for Souders–Brown equation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Souders–Brown equation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Souders–Brown equation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Souders–Brown equation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Souders–Brown equation in simple terms?

Why does Souders–Brown equation matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Souders–Brown equation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Souders–Brown equation.