How Fluid Leaks Out of Containers: The Torricelli Relation

insta: @profbriankirby twitter: @profbriankirby
If you poke a hole in a container filled with fluid, the fluid leaks out. And if the container is big enough and you poke the hole cleanly and you pick the fluids right, the path of the jet that zooms out can be predicted with algebraic equations pretty easily. The path is the same as a ball moving through empty space and the initial velocity is set by the location of the hole.

This model problem, though, is great for challenging students to write the integral form of the Bernoulli equation, and to identify which points in a flow can be linked by streamlines without ever solving for the detailed velocity field. Fluids professors always assume that you can draw the streamlines of a flow so you can apply the Bernoulli equation, but we almost never actually tell you how to do that. I don't think I do in this video either. Yay fluid mechanics!

This video series is called "Professor Kirby's Fluid Mechanics Kitchen" because the instructional design team in the Sibley School of Mechanical and Aerospace Engineering thought "Professor Kirby Teaches Kids to Say No To Drugs" would be misleading. This video was recorded in the Bellis Fluid Dynamics Labs at Cornell. This is the first one we did, right after covid shut everything down, so the "microphone" was Patrick Wick's phone and the "camera" was my phone and the "cinematic backdrop" was a bulletin board or something and I wore a black shirt so you could see the jets and then later I kept wearing the same shirt for continuity and now people think I own only the one shirt.

Lectures are from Cornell University Mechanical Engineering 3230 - Introductory Fluid Mechanics. For reference information, especially how I teach it in MAE3230 at Cornell, see "How Fluids Work", Brian J. Kirby at Amazon: https://smile.amazon.com/dp/B09FRYGMVW.

The music in the series is the music I listened to when I was doing my fluid mechanics homework back when I was in undergrad. In this video, it is Tone Loc "On Fire" and Leaders of the New School "Sobb Story". Did I mention that I was in Kinney Drugs the other day and they were playing Rufus "You Got the Love" and I was like WHAT IS HAPPENING WHY IS THE DRUGSTORE PLAYING A CHICAGO FUNK BAND FROM I DON'T KNOW, 1975 OR SOMETHING. HOW DID THIS HAPPEN. WHO IS THE AWESOME PHARMACIST/DJ SETTING THE PLAYLIST AT THE DRUGSTORE and then I thought actually probably it was just an AI algorithm that was supposed to play Solange but had stopped working, accidentally bringing Chaka Khan back into my life. For those not knowledgeable with Tone Loc's oeuvre and wondering how this specific free-association happened, the good version of "On Fire" samples "You Got the Love". Under no circumstances should you ever listen to the bad version of "On Fire". Tone Loc doesn't carry the song. The Rufus loop carries the song.

I feel I should mention also that for the first draft of this video Patrick sampled "Funky Cold Medina" instead of "On Fire", and I still don't think I have forgiven him for that.