> For the complete documentation index, see [llms.txt](https://wiki.gtpropulsivelanders.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://wiki.gtpropulsivelanders.org/propulsive-landers-gt-docs/wiki/liquid-governing-relations.md).

# Liquid Governing Relations

### Characteristic Length

Characteristic length relates chamber volume and throat area:

$$
L^\*=\frac{V\_c}{A\_t}
$$

or:

$$
V\_c=L^\*A\_t
$$

L\* is mostly chosen based on propellant combination and combustion residence time. It is a sizing rule for making sure the chamber has enough volume for combustion to complete. Typical workflow is to finalize your propellant combination and then lookup Huzel & Huang's book and use the corresponding L\*. 

### Contraction Ratio

Contraction ratio relates chamber area to throat area:

$$
\epsilon\_c=\frac{A\_c}{A\_t}
$$

or:

$$
A\_c=\epsilon\_c A\_t
$$

For small liquid rocket engines, contraction ratio is often around:

$$
\epsilon\_c \approx 3 \text{ to } 8
$$

### Chamber Diameter

For a circular chamber:

$$
D\_c=\sqrt{\frac{4A\_c}{\pi}}
$$

### Chamber Length

Once chamber volume and chamber area are known, chamber length can be estimated as:

$$
L\_c=\frac{V\_c}{A\_c}
$$

If the converging section volume is included separately:

$$
L\_c=\frac{L^\*A\_t - V\_{conv}}{A\_c}
$$

### Liquid Engine Sizing Flow

A simple liquid engine sizing order is:

$$
A\_t=\frac{\dot{m}\_{tot}c^\*}{P\_c}
$$

$$
V\_c=L^\*A\_t
$$

$$
A\_c=\epsilon\_cA\_t
$$

$$
L\_c=\frac{L^\*A\_t - V\_{conv}}{A\_c}
$$


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