The problem is current, not voltage. I/O pins can only manage a maximum of 40mA and you should keep under that if you want your Arduino to have a long life.
Your arduino is a microcontroller. It provides logic not power. If you wish to power something do so using a power supply, depending on your requirements you may already have one for your phone etc. The small voltages and current provided by the arduino can be used to switch the power supply using transistors or mosfets etc.
If you try to get too much current the voltage doesn't "hold" up. The Arduino will overheat and it MIGHT die.
The relationship between voltage, current, and resistance is defined by Ohm's Law. Resistance is "the resistance to current flow". Usually we don't know the resistance of a water pump but given the current rating we could calculate it from Ohm's Law. (The resistance and current will vary depending on the physical load on the motor.)
...If you plug too many high-power things into a power outlet in your house, you'll get excess current and blow a circuit breaker and then the voltage goes to zero until you reset the breaker.
The pins can provide an absolute maximum of 0.2 Watts of power (5V, 40mA). Best limited to 0.1W (20mA). If you need to drive anything that is not 5V or is more than 2mA you need driver hardware like a transistor, MOSFET, H-Bridge...
Electrical Characteristics/specifications of an IO Pin pf ATmega328P Microcontroller.
The meaning of VOH = 4.2V.
When HIGH is asserted on a pin and the load draws 20 mA current, it is guaranteed that the pin will hold minimum 4.2V under the condition that the Vcc supply for the MCU is 5V and the chip's internal temperature does not exceed 850C.
Got it, you're either trolling or keeping your million-dollar idea super-secret.
You've been told that there are no pumps that can be run directly from a pin output. If you don't want to specify a set of requirements, then this thread is a complete waste of time.