Final answer:
Partially covering the end of a garden hose with your thumb increases the water velocity and pressure due to a smaller exit area, enabling the water to squirt farther through the principles described by Bernoulli's Equation.
Step-by-step explanation:
When you squirt water from a garden hose and partially cover the opening with your thumb, you are taking advantage of fluid dynamics, specifically an application of Bernoulli's Equation. By covering part of the hose's end, you reduce the area through which the water can escape, which in turn increases the speed of the water flow due to the conservation of energy. The faster speed of the water leaving the hose results in water being ejected a greater distance. This is because when you apply the same force over a smaller area, which is what happens when you partially obstruct the nozzle with your thumb, you increase the pressure. As a consequence of the increased pressure and velocity of the water, the stream travels farther than it would under normal conditions without any obstruction.
This phenomenon can be partly understood by considering how the pressure inside a hose nozzle can be less than atmospheric pressure, an effect described by Bernoulli’s principle. Since water is a fluid that moves from high to low pressure, when the water speeds up as it passes through the reduced nozzle opening, the pressure drops. Yet, due to the water's kinetic energy, it is able to emerge against the opposing atmospheric pressure and travel a greater distance.