# Flow rate/s for T200?

Hi there, I am using a T200 for a project and don’t have access to a flow meter and would like to know if there is a way to simply calculate the flow rate of the T200 Thruster at a certain thrust.

For example at 12V and 4.6A (according to the graphs on the store page) the thruster generates about 55W of power and a thrust of 2.91Kg f. Is there a way to convert these values to flow rate?

Also is it possible to add a graph of the flow rates to the store page if these values have already been measured?

We don’t currently have the tools and not yet measured the flow rate or flow speed of our thrusters. However, you are right that with some estimates and math we can get to a reasonable rough theoretical value for these, at least under ideal conditions.

The T200 propeller has a 76.2 mm outer diameter, and a 40 mm diameter central hub. It also has a pitch of 22.5° at 75% of its radius, and spins at about 3075 RPM full throttle 12 V, and 3600 RPM 16 V. Using the pitch and and RPM approximation, this results in a theoretical maximum flow speed of 4.45 m/s at 16 V, and 3.80 m/s at 12 V. The propeller has an area of about 0.00330373 m^2. Multiplying these area by the flow speed results in a volume of about 0.014702 m^3/s (or 14.7 liters/s or 3.88 gallons/s) at 16 V, and 0.012554 m^3/s (or 12.5 liters/s or 3.32 gallons/s) at 12 V.

Note that the 55 W power number you mention is not the power generated by the thruster, rather the electrical consumption. The actual mechanical power will be lower due to the efficiency of the thruster.

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. I hope this helps!

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Thank you for such an informative response, it is much appreciated. I only needed rough estimates and this will definitely help.

I would just like to ask if the flow rate would be a linear change with a change in RPM?

Thanks again

Glad to help! Yes, flow rate will be linear with a change in RPM.

Might be a simple question but is the RPM also linear to the PWM signal? So for instance will the RPM change linearly between the reverse PWM range of 1100us - 1500us?

(I am trying to figure out what RPM the motor is running at a certain PWM, so i can then roughly calculate the flow rate from what you said previously).

Thank you in advance!
Joshua

Hi Joshua,

Take a look in this post, this may be useful for you:

Doing some fitting with a linear equation, you can find that RPM/PWM can be approximately linear, but it depends if the margin of error is ok for you. A 3rd order one could be more precise for you: Hi @adam . Thanks for the calculation. It is very informative. My question is does this calculation is made for 16V, 24A, 390 W values?

Thanks.

Thank you theoretical maximum flow speed calculation.

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… how can we convert this into inches… I am electronics background, didn’t know the much details regarding this… Please explain the step by step process how u got 4.45m/s…

Thank you…

Hi @shakeera,

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:

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,

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 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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Dear Eliot,

Thank you so much for the detailed explanation.
It helps a lot to understand the flow speed calculations.

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