user49575: I want to know if I could connect many Arduino Nano  boards together (Example : 10 boards ) , Also i want to know  if there is any problem in Communication between them  using I2C , could this affects processing speed on every board ,  and  if there's going to be any kind of delay when communicating?

user20245: 
I want to know if I could connect many Arduino Nano boards together...

Yes, you can read about it here at arduino.cc. Where is says: "...it can be helpful to set up two (or more!) Arduino ... boards to share information with each other..."

... i want to know if there is any problem in Communication between
  them using I2C ...

This feature, according to the above link, is expected to work.  (Can you explain the type of problems you are avoiding?)

...could [i2c communication] affect processing speed on every board ...

Most likely it will.  Most Arduino platforms do not run operating systems.  So your program is all that is running.  If your program is busy sampling sensors, it will be difficult (not impossible) to concurrently handle i2c communications.

user47766: Yes it certainly is possible. And can work well if done properly. The concern that I have is when longer wiring lengths are used. I2C is not intended for extended distributions. And if that were the plan then I STRONGLY advise using proper I2C buffer chips designed for that purpose. 
The more devices, the more wire, all adds to the capacitance on the lines. Because I2C uses pull up resistors to produce a high the added capacitance limits either the length of wire that can be used, or the transmission frequency. I have used I2C buffers in may products and it is very useful when extended length is required. I use both I2C buffers, and also I2C isolated buffers. The company I work for manufactures distributed control electronics. I am one of the hardware designers. I have been using I2C like this for about 15 years.
For now have a look at this web page.  http://www.techbitar.com/how-to-network-many-arduinos-with-sensors-using-i2c.html
I'm sure it will spur some questions. It makes things simpler if there is only one master controlling the communications bus. Multimast is possible but can have more conflicts and you then need to deal with that issue. Best not to go there.
I2C is not a very robust protocol but still can be usable between processors if handled carefully. Keep it simple. 

49575: <p>I want to know if I could connect many Arduino Nano  boards together (Example : 10 boards ) , Also i want to know  if there is any problem in Communication between them  using I2C , could this affects processing speed on every board ,  and  if there's going to be any kind of delay when communicating?</p>
 20245: <blockquote>
  <p>I want to know if I could connect many Arduino Nano boards together...</p>
</blockquote>

<p>Yes, you can read about it <a href="https://www.arduino.cc/en/Tutorial/MasterWriter" rel="nofollow noreferrer">here at arduino.cc</a>. Where is says: "...it can be helpful to set up two (or more!) Arduino ... boards to share information with each other..."</p>

<blockquote>
  <p>... i want to know if there is any problem in Communication between
  them using I2C ...</p>
</blockquote>

<p>This feature, according to the above link, is expected to work.  (Can you explain the type of problems you are avoiding?)</p>

<blockquote>
  <p>...could [i2c communication] affect processing speed on every board ...</p>
</blockquote>

<p>Most likely it will.  Most Arduino platforms do not run <a href="https://en.wikipedia.org/wiki/Operating_system" rel="nofollow noreferrer">operating systems</a>.  So your program is all that is running.  If your program is busy sampling sensors, it will be difficult (not impossible) to concurrently handle i2c communications.</p>
 47766: <p>Yes it certainly is possible. And can work well if done properly. The concern that I have is when longer wiring lengths are used. I2C is not intended for extended distributions. And if that were the plan then I STRONGLY advise using proper I2C buffer chips designed for that purpose. </p>

<p>The more devices, the more wire, all adds to the capacitance on the lines. Because I2C uses pull up resistors to produce a high the added capacitance limits either the length of wire that can be used, or the transmission frequency. I have used I2C buffers in may products and it is very useful when extended length is required. I use both I2C buffers, and also I2C isolated buffers. The company I work for manufactures distributed control electronics. I am one of the hardware designers. I have been using I2C like this for about 15 years.</p>

<p>For now have a look at this web page.  <a href="http://www.techbitar.com/how-to-network-many-arduinos-with-sensors-using-i2c.html" rel="nofollow noreferrer">http://www.techbitar.com/how-to-network-many-arduinos-with-sensors-using-i2c.html</a></p>

<p>I'm sure it will spur some questions. It makes things simpler if there is only one master controlling the communications bus. Multimast is possible but can have more conflicts and you then need to deal with that issue. Best not to go there.</p>

<p>I2C is not a very robust protocol but still can be usable between processors if handled carefully. Keep it simple. </p>
