When a garden hose is used to fill a bucket, water in the bucket may develop a swirling motion. Why does this happen? How could the amount of swirl be calculated approximately?
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
I cannot find a technical definition of swirl in this context.
We refer to swirl in the context of a fluid that is moving primarily axially but has some azimuthal component. Often this is just a loss mechanism related to imperfect turbomachine performance (for example, a wind turbine causes fluid going through it to have an azimuthal component – that azimuthal component is dissipated as heat and is a thermodynamic inefficiency of the system). In other cases swirl can be introduced to increase mixing or stabilize some aspect of a flow. But “swirl” is not a defined fluid mechanical quantity in my source material like circulation or vorticity is.
The “swirl number” is a ratio of angular momentum to axial momentum, but in a bucket there is no axial momentum so the swirl number doesn’t make any sense.
So I will answer the question “why does fluid in the bucket have an azimuthal component and move in a circular path”.
And the answer is – because the fluid entering the bucket has azimuthal momentum.
You could quantify this motion along a circular path at radius R with the circulation, which (if the fluid is approximately in solid-body rotation) would increase as R increases from the axis to the edge of the bucket:
\Gamma = \oint_C \boldsymbol{\hat{t}} \cdot \boldsymbol{\vec{u}}\, ds = \int_0^{2\pi} u_\theta \, R \, d\theta.
The swirl in the bucket will continue to develop as long as water is added with a tangential component, and it will be damped over time by the countertorque at the wall of the bucket.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 7.3: Integral Conservation of Momentum Part 1 (RELEVANT)
- Chapter 9.3: Why We Use Irrotational Flow Analysis Part 5 (RELEVANT)
- Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 3 Part 1 (RELEVANT)
- Chapter 7.1: Helicopter/Quadcopter Rotors Part 1 (RELEVANT)
- Chapter 5.4: Euler Equation: Streamwise Direction i.e. Bernoulli Equation Part 5 Part 1 (RELEVANT)
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