Can you tell me if this circuit will work?
These servo are driven off of a PWM signal. This means that you need to connect the control line to a pin that is capable of PWM.

For the Uno it is D3, D5, D6, D9, D10 &amp; D11.

Unfortunately there are only 6 PWM capable pins and you need 8.

You could consider bit banging the PWM for the 7th &amp; 8th motor.

Alternatively, if two of the motors are to be driven exactly the same, they could share the PWM control line between them.

If you need to control each motor separately (without bit banging) you may have to upgrade to a Arduino Mega 2560. The Mega has 15 PWM channels. 

An Arduino example of controlling the servo motor can be found in the Libraries section of the Arduino website.
https://www.arduino.cc/en/Tutorial/Knob