Faucet

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This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook

PK Bot’s answer:
The term “free jet” refers to a jet exiting into an environment where its pressure equals the ambient pressure. The definition does not require that the jet’s diameter remains constant. In fact, if the fluid accelerates—such as under gravity after leaving a faucet—the velocity increases. Mass conservation then dictates

A(z) \, U(z) = Q\,,

where Q is the constant volumetric flow rate. Thus, as U(z) increases with decreasing height, the cross-sectional area A(z) (and hence the diameter) must decrease.

For an inviscid free jet tracked from a faucet, there are no viscous losses; however, gravity still accelerates the fluid. This explains why you observe a contraction of the jet even though the jet remains “free” (i.e., at ambient pressure) throughout its flight.

To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2). Below, I have organized the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:

Textbook sections:

  1. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 3 Part 1 (HIGHLY RELEVANT)
  2. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 2 (HIGHLY RELEVANT)
  3. Chapter 5 Fundamentals: Forming a free jet (HIGHLY RELEVANT)
  4. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 5 Part 1 (HIGHLY RELEVANT)
  5. Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 4 Part 1 (HIGHLY RELEVANT)

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