Final answer:
Placing your thumb over the end of a garden hose and then releasing it results in a greater squirt distance due to a decrease in pressure and an increase in velocity, in accordance with Bernoulli's principle and the continuity equation.
Step-by-step explanation:
Understanding Water Squirt Dynamics in a Garden Hose
When you place your thumb over the end of a garden hose and then release it, the water is squirted a greater distance due to a change in pressure and velocity. This is explained by Bernoulli's equation and the continuity equation. By partially covering the end of the hose, you decrease the cross-sectional area through which the water can escape, while the volume of water trying to get out remains the same.
According to Bernoulli's principle, a decrease in the cross-sectional area leads to an increase in the fluid's velocity. Since the water pressure must push the same amount of water through a smaller area, the velocity of the water increases to maintain the flow rate. This increased velocity allows the water to be squirted further. The correct answer to the provided question is a) Decreases pressure, increasing velocity.
Pressure and velocity are inversely related in this scenario. Reducing the opening increases the speed of the water as it must move faster to exit through the smaller opening, and this faster-moving water has a lower pressure according to Bernoulli's principle. Consequently, the water squirts out at a higher velocity and travels a larger distance.