Bernoulli's equation and a stream of water

[ttk3]

Homework Statement

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). Hint: Think about the change in velocity and the change in pressure as the water falls.

Homework Equations

P₁+.5pv²₁+pgy₁=P₂+.5pv²₂+pgy₂

The Attempt at a Solution

As the water falls the velocity should increase so the pressure should decrease. Wouldn't a decrease in pressure cause the water to spread out near the bottom?

 

[Gear300]

Note that in Bernoulli's equations you have K/V and U/V on both sides, K being kinetic energy, U being potential energy, and V being volume. delta(K) = -delta(U); taking that into account, P1 = P2.

There is a continuous volume flow for ideal fluid flow. So A1v1 = A2v2. At the bottom, v2 > v1 and so A2 < A1.