MediumPhysicsHigh School (11–12)Mechanics › Fluid Flow, Bernoulli's Principle and ViscosityNumerical
A tank on the ground holds water 2.8 m deep.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A tank on the ground holds water deep. A small hole can be made in its side at any depth. At what depth does the jet land farthest from the tank, and how far does it reach? How fast is that jet? (.)
Need a reminder? The key ideaShow
Torricelli's law: water leaves a hole below the surface of an open tank at . A Venturi meter finds the speed of flow from the pressure drop in its throat. Fast air has low pressure, which lifts wings and roofs.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Range. Speed , fall , so the range is .
Step 2. Best depth. The product is largest at , giving a range of .
Step 3. Speed. .
Answer: Halfway down, ; it reaches , equal to the depth of water; the jet moves at .
Watch out. The deepest hole gives the fastest jet but the shortest fall.
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