How to Calculate the Speed of a Sprocket?

In summary, there is not enough information provided to calculate the speed of the sprocket connected to the turbine shaft of a cross flow turbine. The efficiency of the turbine, net head, volume flow rate, and specific weight of water are given, but the load on the turbine and the design characteristics of the turbine are unknown. Additionally, the friction resistance will increase with speed and can ultimately lead to self-destruction if the turbine is not properly designed.
  • #1
Ballena Joseph
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How to calculate the speed of sprocket connected to the turbine shaft of a cross flow turbine if I only have these given parameters: Net Head, Volume Flow Rate, Specific Weight of Water and Efficiency of Cross Flow Turbine? Does the Cross Flow Turbine, Turbine Shaft and Speed of Sprocket have the same speed? Then, what formulas should I use to finally compute the speed of Sprocket?
 
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  • #2
Ballena Joseph said:
How to calculate the speed of sprocket connected to the turbine shaft of a cross flow turbine if I only have these given parameters: Net Head, Volume Flow Rate, Specific Weight of Water and Efficiency of Cross Flow Turbine? Does the Cross Flow Turbine, Turbine Shaft and Speed of Sprocket have the same speed? Then, what formulas should I use to finally compute the speed of Sprocket?
I think, if the efficiency is given, power out of the turbine can be calculated by using the water power.Then the rpm of the shaft can be calculated from the output power.
If the sprocket is attached to the shaft with a key, then it should rotate at the same speed as the shaft.This is for no load condition.
 
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  • #3
How is the sprocket connected? Via a belt? a gear?

In this thread, and your previous thread, you did not mention the load on the turbine. What is the turbine driving? The more mechanical load you put on the turbine, the slower the RPM for the same power.
 
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  • #4
The rpm always depends on the torque output.

What you know is the power output. In your case it is ##P = \eta\rho g h \dot{V}##, where ##\eta## is the efficiency of your turbine, ##\rho## is the fluid density, ##g## is the acceleration due to gravity and ##\dot{V}## is the volume flow rate. This will always be constant.

As @anorlunda mentioned, you then need to know the load you will put on your turbine, i.e. what is the torque output ##T##? Then ##rpm = \frac{P}{T}##. If you put no load on the turbine, then it will accelerate until it reaches a sufficient load ... or until it self-destructs.
 
  • #5
Ballena Joseph said:
How to calculate the speed of sprocket connected to the turbine shaft of a cross flow turbine if I only have these given parameters: Net Head, Volume Flow Rate, Specific Weight of Water and Efficiency of Cross Flow Turbine? Does the Cross Flow Turbine, Turbine Shaft and Speed of Sprocket have the same speed? Then, what formulas should I use to finally compute the speed of Sprocket?
It can't be calculated with the information given. The rotation speed of a turbine is dependent on the specifics of the design of the turbine and does not have an easy analytical solution unless you already know every other directly related parameter about the turbine's performance (and you know almost nothing about the turbine; mostly you just know about the water).

This question has the feel of being a part of a larger issue becuase it isn't a very meaningful/useful question in and of itself. Is this a real world problem? Please tell us what the real problem is.
 
  • #6
jack action said:
If you put no load on the turbine, then it will accelerate until it reaches a sufficient load ... or until it self-destructs.

Does this mean, the friction resistance will be the only load.Since it is comparitively small, the turbine will attain very high speeds and after a limit it self destructs due to the high temperature attained(due to friction)?Does the friction resistance increases with speed?
 
  • #7
Mohankpvk said:
Does this mean, the friction resistance will be the only load.
Yes.

Mohankpvk said:
Since it is comparitively small, the turbine will attain very high speeds and after a limit it self destructs due to the high temperature attained(due to friction)?
Yes. But sometimes, the turbine could be so off from its design characteristics, that the power output will be significantly lowered before self-destruction is reached.

Mohankpvk said:
Does the friction resistance increases with speed?
Yes. Just considering a simple bearing, you can see that speed is a factor.
 
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  • #8
You said you know the volume flow rate through the turbine. Do you also know the volume per revolution of the turbine?
 
  • #9
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The speed won't increase forever, no matter how little friction you have. There will be a speed at which no more power is extracted from the water in this arrangement because the vertical velocity of falling water will match the vertical component of the blade at the given blade angle. You can't make that exact balance simultaneously on both the top and bottom blades because the water velocity is different top and bottom. However, you can see that energy extracted from the water (thus turbine efficiency) will vary greatly with wheel speed with efficiency approaching zero at "high" speed.

So, to add to what @russ_watters told you, there's not enough information to do the calculation. One of the missing things is the shape and angle of the blades.If this is a school project, I suggest that you do experiments rather than calculations.
 

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1. How do I calculate the speed of a sprocket?

To calculate the speed of a sprocket, you need to know the pitch diameter and rotational speed of the sprocket. You can use the formula: speed = (pitch diameter x pi x rotational speed) / 12. For example, if a sprocket has a pitch diameter of 6 inches and a rotational speed of 100 revolutions per minute, the speed would be (6 x 3.14 x 100) / 12 = 157 feet per minute.

2. What is the pitch diameter of a sprocket?

The pitch diameter of a sprocket is the diameter of the circle formed by the center of the sprocket teeth. It is typically measured from the center of one tooth to the center of the tooth directly opposite it.

3. How do I find the rotational speed of a sprocket?

The rotational speed of a sprocket can be measured in revolutions per minute (RPM) or radians per second (rad/s). You can use a tachometer to measure the RPM of a sprocket or calculate it by measuring the time it takes for the sprocket to complete one full revolution.

4. Can the speed of a sprocket vary?

Yes, the speed of a sprocket can vary depending on its rotational speed and pitch diameter. A larger pitch diameter or higher rotational speed will result in a faster speed, while a smaller pitch diameter or lower rotational speed will result in a slower speed.

5. How accurate is the speed calculated using the formula?

The speed calculated using the formula may not be completely accurate due to factors such as friction and wear on the sprocket teeth. However, it can provide a good estimate of the sprocket's speed and is commonly used in engineering and design calculations.

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