Reader Questions

Pascal’s Barrel Follow-Up

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fuckyeahfluiddynamics:

Pascal’s Law tells us that pressure in a fluid depends on the height and density of the fluid. This is something that you’ve experienced firsthand if you’ve ever tried to dive in deep water. The deeper into the water you swim, the greater the pressure you feel, especially in your ears. Go deep enough and the pressure difference between your inner ear and the water becomes outright painful.

In the video demonstration above, you’ll see how a tall, thin tube containing only 1 liter of water is able to shatter a 50-liter container of water. Not only does this show just how powerful height is in creating pressure in a fluid, but it shows how a fluid can be used to transmit pressure over a distance – one of the fundamental principles of hydraulics! (Video credit: K. Visnjic et al.; submitted by Frederik B.)

Reader @hoosierfordman77 writes:

“They’re pressurizing the line by using a syringe sealed to the tube.  Of course, the volume of water in the tube added to this.  But it was not the only source of pressure.  Also explaining that pressure only has one vector as in the illustration using Hoover Dam is preposterous.  Sir [sic] later stated correctly that pressure is evenly distributed through the inside of a container.  If her demonstration was correct then the pressure of the water in lake Meade is not proportional to the volume of the lake…only proportional to its depth.  Now I’ve not done testing but I do not believe a 100,000 acre lake that’s 1 foot deep would be held back by the walls of a kiddie pool that routinely handle that depth.” (emphasis added)

Hi, hoosierfordman77, thanks for your comment! It does seem counter-intuitive that pressure in a reservoir is proportional to depth, not volume, but it is correct. If you go swimming 1 meter below the water surface, the pressure you experience is the same whether you’re in a backyard pool or the Gulf of Mexico. And, yes, a 100,000 acre lake that’s 1 foot deep has a static pressure that could be withstood by a kiddie pool.

Now engineers don’t build it that way for a couple of reasons. 1) Pascal’s Law only describes hydrostatic forces – that is, the force experienced when the water is motionless. In reality, a dam would need to withstand not only the hydrostatic forces caused by the water’s depth but also any forces exerted when the water moves due to wind action, temperature differences, etc. And 2) after evaluating all of the expected forces a structure will endure, engineers add a factor of safety to make the structure strong enough to withstand forces above and beyond what is expected in ordinary or extraordinary operation.

As for the syringe, it only adds additional pressure to the line if they do not allow a gap for air in the line to escape. That can be a bit of a challenge, as they acknowledge in the video when they discuss the effects of air bubbles in the line. However, there is every indication that they were aware of this potential in their demonstration and did everything they could to ensure that it was not affecting the result. The fact remains, however, that extra pressure in the line is unnecessary – the 1 liter of water’s depth alone will shatter that container.

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