Plugs Safety
Posted on Monday, January 5th, 2009 at 5:17 pm
How many liters of water come out? ….Physics Fluid question.?
A cylindrical steel pressure vessel with volume 1.47 m^3 is to be tested. The vessel is entirely filled with water, then a piston at one end of the cylinder is pushed in until the pressure inside the vessel has increased by 3000 kPa . Suddenly, a safety plug on the top bursts.
How many liters (L) of water come out?
Let’s see. We may assume that the compression of the water is the dominant contributor to the internal pressure, and that the weight of the water contributes little.
Bulk modulus of water, Β = V*ΔP / ΔV
When water is initially poured in, we’ll call that the equilibrium state. There will be stresses set up due to the weight of the water, however the top of the vessel (where the plug is) will experience no stress or pressure.
Then the water is compressed by the piston. Two things are going to happen. The piston is going to decrease the length of the cylinder, thus increasing the internal water pressure. This internal pressure is then going to cause the walls of the container to expand under stress. This is the only stress that the plug feels.
You haven’t given any information on the dimensions of the container, so it’s hard to take into account the expansion of the wall. So let’s ignore that for now. We take the container as being rigid.
For the pressure to increase by 3e6 Pa, the water must be compressed by an amount
ΔV = V*ΔP / Β = 1.47*3e6 / 2.2e9
= 0.002 m^3 = 2 L
Now the pressure is 3 MPa. The plug bursts allowing water to escape until there are no more stresses at the top i.e. until only gravity effects exist once again. Once we are reduced to the initial gravity state, there is no longer any driving force for water to escape from the top.
This means that 2 L of water that must escape before the initial equilibrium is restored.
The only thing that bothers me still is that the question specifically mentioned that the vessel is made of steel, which indicates that wall expansion may be an issue that affects this result. In order to consider the elasticity of the container, we need to know the value of R/t, the radius to thickness ratio. If we use R/t = 10 with properties of steel, we’ll find that 2.44 L of water escape instead.
Here’s a follow up question if you’re interested.
http://answers.yahoo.com/question/index;_ylt=Ah6X0FC4qjh0w16E4QppFxPsy6IX;_ylv=3?qid=20080715113424AAycCTs
|
|
Hamilton Beach 40898 Cool-Touch Cordless 8 Cup Electric Kettle $42.88 Tea? Hot chocolate? Instant soup? If you have a taste for it, a Hamilton Beach Kettle can have it ready in minutes. Incorporating the best of Good Thinking, the powerful rapid-boil system provides fast heat-up from any standard outlet and the auto shutoff function helps keep it from boiling dry. Hamilton Beach Kettles are great looking and easy to use. Plus, most models include a 360-degree rotati… |
|
|
Presto Pressure Cooker Sealing Ring/Overpressure Plug Pack (4 & 6 Quart) $4.50 For Presto pressure cookers and canners. Fits model… |
|
|
KitchenAid Gourmet Essentials 2-Quart Tea Kettle, Stainless Steel $40.99 KitchenAid’s new Gourmet Essentials teakettle holds 2-quarts, giving you plenty of hot water for your soups or beverages. This new line combines beautiful porcelain enamel-coated exteriors with the brilliance of stainless steel found on the lids and handles. In a delightful Brushed Stainless color, the teakettle has sturdy handles covered in matching, heat-resistant silicone that offer cooks a fir… |
|
|
Parts Water $15.98 … |
|
|
Parts Water $15.99 … |
|
|
Parts Water [Vinyl] $15.98 … |
|
|
3M 90541-80025T TEKK WorkTunes Hearing Protector and AM/FM Radio $40.74 Protect your ears while keeping yourself motivated at your job site with your favorite tunes or radio programming with the 3M TEKK 90541-80025T WorkTunes with digital tuning hearing protector, which includes an integrated AM/FM radio and a stereo input jack for connecting an MP3 player. A great choice for use on construction sites (check your local regulations), in your workshop, or in your yard w… |
|
|
Belkin Mini Surge Protector Dual USB Charger $12.99 Protect your electronic devices while traveling…. |
|
|
Howard Leight R-01526 Impact Sport Electronic Earmuff $73.23 To capture low level sound, the Impact Sport employs built-in microphones that amplify range commands and other important sounds. Users enjoy full, clear directional hearing in stereo. For protection, the Impact Sport actively listens and automatically shuts off amplification whenever harmful sound levels are reached. The earmuffs effectively block any noise, continuous or impulse, of 82dB or more… |
|
|
SANYO 4-Position Ni-MH Rechargeable Battery Charger $12.99 Eneloop batteries offer exceptional shelf life so you can use your rechargeable batteries when and where you need them most. You can charge your eneloop batteries once, store them away for up to three years and use them at a moment’s notice. After charging eneloop batteries they will maintain 75% of their capacity for up to three years. They are ready to be used immediately right out of the pack. … |