# Flow rate/s for T200?

**URL:** <https://discuss.bluerobotics.com/t/flow-rate-s-for-t200/4117>\
**Category:** Thrusters and Motors\
**Created:** [January 21, 2019, 6:19am UTC](https://discuss.bluerobotics.com/t/flow-rate-s-for-t200/4117 "2019-01-21T06:19:30Z")\
**Posts on this page:** 1\
**Showing post:** 9

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**Author:** ![EliotBR](https://sea1.discourse-cdn.com/flex019/user_avatar/discuss.bluerobotics.com/eliotbr/32/6937_2.png) [@EliotBR](https://discuss.bluerobotics.com/u/EliotBR)\
**Post date:** [May 6, 2022, 9:54am UTC](https://discuss.bluerobotics.com/t/flow-rate-s-for-t200/4117/9 "2022-05-06T09:54:18Z")

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Hi @shakeera,

> [@shakeera](#):
>
> Can you please give the step by step calculation using pitch and rpm… somewhere I saw pitch into rpm multiplication but here pitch in degrees…

The “pitch” being discussed here is the pitch angle of a single blade relative to the rotation plane of the propeller - “\theta” in the section cut in the following diagram:

 ![image](https://us1.discourse-cdn.com/flex019/uploads/bluerobotics/original/2X/3/36149caf164f679f516abb9bf2f37562077acbc7.png)

As the propeller spins, each blade can be thought of as moving through the water like the thread of a screw. In an ideal case (with no “slip”), the maximum flow velocity is exactly equal to the offset between the rotational velocity and the pitch angle:

v\_\text{max-flow} = v\_\text{rot}\cdot \tan{\left(\theta\right)}

Rotational velocity is determined by the angular rotation rate at a given radius

v\_\text{rot} = \frac{\text{RPM}}{60\frac{\text{seconds}}{\text{minute}}} \times 2\pi r'\ \frac{\text{m}}{\text{revolution}}

75% of the propeller’s tip radius is a common value for estimating propeller speed and flow rate, so

\begin{align} r'&= 0.75\times r\_o\\ &= 0.75\times 38.1\text{ mm}\\ &\approx 0.0286\text{ m}\\ \rightarrow v\_\text{rot} &\approx \frac{3600}{60\text{ s}}\times 2\pi \times 0.0286\\ &\approx 10.77\ \frac{\text{m}}{\text{s}}\\ \rightarrow v\_\text{max-flow} &\approx 10.77 \times \tan{\left(22.5^\text{o}\right)}\\ &\approx 4.46\ \frac{\text{m}}{\text{s}} \end{align}

Substituting in the 12V RPM instead gives 3.81 m/s.

As @Adam mentioned though,

> [@adam](#):
>
> Bear in mind these speeds and flow rates are rough estimates based on some math and not true measurements, I would expect the real number to be lower. However, they should be reasonably accurate for estimation purposes.

Given the rough and maximal/ideal nature of the values, rounding down to the nearest 0.05 m/s seems reasonable to avoid too much false/inaccurate precision.

Note also that realistic flow rates [depend on the relative incoming speed](https://discuss.bluerobotics.com/t/t200-performance-with-relative-speed/11373) between each thruster and the water going through it, which is not considered or accounted for in the “theoretical maximum” calculations presented here.

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