# Max linear speed of propeller tip in water

• james weaver
In summary, the maximum propeller speed is determined by the radius of the propeller, the speed of the water flow, and the angle of attack of the blade profile.
james weaver
Homework Statement:: project not homework
Relevant Equations:: vectors

Hi,I am trying to determine the maximum linear velocity of a propeller tip when subject to flowing water with velocity ##\vec V##. For simplicity, I will assume that rotational inertial is negligible. The drawing below shows the tip of a propeller blade as viewed directly level from the side. If the following diagram is correct, it implies that the maximum of ##\vec Vsin\theta cos\theta## will occur when ##\theta## is at 45 degrees, and will be equal to exactly ##\frac 1 2\ \vec V##

The relationship seems reasonable as ##\vec Vsin\theta cos\theta## is zero when ##\theta## equals 0 or 90, which is expected.

james weaver said:
Homework Statement:: project not homework
Relevant Equations:: vectors

Hi,I am trying to determine the maximum linear velocity of a propeller tip when subject to flowing water with velocity ##\vec V##. For simplicity, I will assume that rotational inertial is negligible. The drawing below shows the tip of a propeller blade as viewed directly level from the side. If the following diagram is correct, it implies that the maximum of ##\vec Vsin\theta cos\theta## will occur when ##\theta## is at 45 degrees, and will be equal to exactly ##\frac 1 2\ \vec V##

The relationship seems reasonable as ##\vec Vsin\theta cos\theta## is zero when ##\theta## equals 0 or 90, which is expected.

View attachment 301675
(Thread moved from HH to ME, since it appears to be a general project question).

When you say "max propeller speed", do you mean for a drive propeller which you are trying to avoid cavitation? Or do you mean for an energy conversion turbine that is being driven by the water flow?

Energy conversion driven by water flow

james weaver said:
Energy conversion driven by water flow
So this is a turbine driven by water, not a propeller moving the water.
There will be twist along the blade. The tip of the blade will trace a helical path in the passing fluid. It is the length of that helix that determines the tip velocity.
Are you assuming that no energy is being extracted from the flow?
What will be the angle of attack of the blade profile when operating?

berkeman
Sorry, I am not very familiar with some of these concepts. For one, I am just assuming that the propeller blades are rectangles that are at a 45 degree angle relative to the axis of rotation of the shaft. Secondly, since I don't have info on the rotational inertia of the shaft, I am trying to determine what RPM would result from this setup (just a rough estimate) given a water velocity of ##\vec V##. My thought process was this: If I want to achieve a given RPM, then what should should the radius of my propeller be? (assuming that the propeller blades were to offer negligible resistance to being rotated).

This is what I have:

##r=\frac {V} {\omega}=\frac { | \vec V sin\theta cos\theta |} {\omega}##

So then ##r## as a function of RPM should be:

##r=\frac { | 30\vec V sin\theta cos\theta |} {RPM\pi}##

Hope this makes sense.

james weaver said:
If I want to achieve a given RPM, then what should the radius of my propeller be?
Firstly, stop calling it a propeller if it is actually a turbine, because it is driven by the fluid.
Secondly, inertia is not important, the detailed problems will come when you begin to extract energy from the flow.
Thirdly, from the bulk fluid and energy side of the problem, a propeller or a turbine can be modeled as a "transducer disc", ignoring the internal details.

Simple analysis says for 45° the tip will rotate about the centre at the same speed as the water flow. That means the water will flow along the tip surface at √2 = 1.4142 times the flow velocity.

But the distance around a circle is 2πr, so the shaft will turn once for each 2π radii of fluid that flows through the transducer disc.

I'm sorry, I'm confused on how the water could flow across the tip surface at a greater velocity than it's initial velocity.

james weaver said:
I'm sorry, I'm confused on how the water could flow across the tip surface at a greater velocity than it's initial velocity.
The length of the tip surface that passes a water molecule is longer than the linear flow down stream, because it is the vector sum of rotation and flow.

Ok, I understand the math. I guess I'm just confused then as to what force accelerates the water from ##\vec V## to ##\sqrt2\vec V##. Guess I have something to learn about fluid dynamics.

james weaver said:
Guess I have something to learn about fluid dynamics.
We are all in that position, always.

The water moves at a fixed speed. The blade rotates at a fixed speed. The contact between the turbine blade and the water is in shear. The differential velocity across that laminar flow is greater than the linear flow of the water downstream. The wetted area surface drag is dependent on blade angle.

Easy version:

Since the blade is rotating, it moves at an angle (depending on its pitch) to the water flow.

The result is you have the water flowing thru the turbine at some speed and the blade tip moving across the water flow. These two add by vector addition.

Since you chose a blade angle of 45°, you can think in terms of a square with one side being the water flow speed and an adjacent side being the blade tip rotational speed. If you draw a diagonal in the square, the diagonals length is the vector sum of the two speeds.

That's why the tip speed thru the water is faster than the straight-line water flow rate.

Hope this helps!

Cheers,
Tom

Last edited:
Thanks guys for these very helpful responses.

berkeman and Tom.G

## 1. What is the definition of the max linear speed of propeller tip in water?

The max linear speed of propeller tip in water refers to the maximum speed at which the tip of a propeller can move through water. It is an important factor in determining the efficiency and performance of a propeller.

## 2. How is the max linear speed of propeller tip in water calculated?

The max linear speed of propeller tip in water is calculated by multiplying the rotational speed of the propeller (in revolutions per minute) by the circumference of the propeller tip. This calculation takes into account the diameter of the propeller and the speed at which it rotates.

## 3. What factors affect the max linear speed of propeller tip in water?

There are several factors that can affect the max linear speed of propeller tip in water. These include the design and shape of the propeller, the size and number of blades, the power of the engine, and the density and viscosity of the water.

## 4. Why is the max linear speed of propeller tip in water important?

The max linear speed of propeller tip in water is important because it directly affects the performance and efficiency of a propeller. A higher max linear speed can result in faster speeds and better fuel efficiency, while a lower max linear speed may result in slower speeds and decreased efficiency.

## 5. Can the max linear speed of propeller tip in water be increased?

Yes, the max linear speed of propeller tip in water can be increased by making changes to the design of the propeller or by increasing the power of the engine. However, it is important to note that increasing the max linear speed may also have an impact on other factors such as noise levels and vibrations.

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