I am planning to work on a art installation which requires changing the speed of water of the water pump from varying digital inputs. The speed of the water pump will be depending on the digital input from a camera input, detecting the number of people entering a given space. e.g. The more people entering, the faster the speed of water emission. I have researched that submerisble pumps and control valve are to be used, however, I wonder if there are any simpler methods. I am relatively new to arduino too, hope u can help!
I assume it's an electrical water pump. From the Arduino point of view this is essentially an electric motor. There are plenty of ways to control these from an Arduino but the options available to you depend on the type of electric motor involved. If it's an ordinary brushed low voltage DC motor then you can control them using an electronic motor driver circuit and it's just a matter of finding a driver compatible with the voltage and current required by the motor. This option would enable variable speed control using pwm.
You mentioned a camera as one of the inputs. This part is likely to be by far the most complex part of your project and sounds likely to involve complex video processing algorithms. You will need to implement and run those on a PC. In this case the only role of the Arduino would be to provide an interface between the external hardware such as switches and motors, and the main control logic on the PC.
If you have a light blue floor and put the camera on the ceiling looking down, counting the number of people is just counting pixels that are not light blue.
Almost al people have black red brown blond hair or are bold, but only few are blue (OK smurfs are, but they wear a white had ;).
If you take a 320x200 webcam (64000 pixels) and lets say an average person takes 30x30 =~900 pixels then you can count pixels and divide by 900 to have a good estimate of the number of people.
A raspPI with python, the PIL library should be enough to get it running.
Try placing an ultrasonic sensor at the top of the door and recording how many times the distance gets a little closer than the distance from the floor. You can use a transistor to control the speed of the water.