A continuous stream of water is flowing out of a faucet and falling into a sink below. Explain why this stream of water is narrower at the bottom (near the sink) than at the top (near the faucet).
The phenomenon you are observing is known as the Venturi effect. The narrowing of the stream of water at the bottom is caused by the conservation of mass and the principle of Bernoulli's equation.
To understand why this happens, let's break it down step by step:
1. Conservation of mass: The amount of water passing through any given point in the stream of water must be constant, assuming there are no leaks or blockages. In other words, the volume of water per second that flows through any section of the stream should be the same.
2. Bernoulli's equation: Bernoulli's principle states that as the velocity of a fluid (in this case, water) increases, its pressure decreases. Similarly, when the velocity decreases, the pressure increases.
Now, let's apply these principles to the flow of water from the faucet to the sink:
As the water flows out of the faucet, it starts with a certain velocity and spreads out into a wider stream. Due to conservation of mass, the same amount of water needs to pass through every point in the stream. Therefore, as the stream widens, the water has to move faster to maintain the constant flow rate.
According to Bernoulli's principle, as the water speeds up, its pressure decreases. This decrease in pressure creates a pressure difference between the fast-moving water in the center of the stream and the slower-moving water on the sides. This pressure difference causes the outer water to be pushed inward, leading to convergence of the stream toward the center.
As the water falls downward, the stream narrows further due to the increased velocity and the resultant decrease in pressure. By the time the water reaches the bottom and falls into the sink, it has formed a narrower stream.
In summary, the narrowing of the water stream near the sink is a result of the conservation of mass and the principles of Bernoulli's equation, causing the water to accelerate and the pressure to decrease, leading to the convergence and narrowing of the stream.
There is a law on this. It is called the law of continunity, or the law of mass continuity.
the amount mass flowing in the stream is density*areastream*velocity.
So if velocity of a falling stream increases, what happens to the area of the stream?