Calculating Pressure and Steam Jet Velocity in a Boiling Pot

In summary: This is the density of your jet. You'll need the velocity of your jet. You can figure this out by using the area of the hole (via its diameter) and the rate at which steam is escaping (0.1 g s^{-1}). You'll also need to consider the pressure difference between the inside of the pot and the outside, as this will affect the velocity of the jet. Once you have all of this information, you can plug it into Bernoulli's equation to solve for the pressure difference. This pressure difference should match the pressure calculated in part (a). In summary, the conversation discusses a pot of boiling water with a heavy lid that has a small hole for steam to escape.
  • #1
tweety1234
112
0

Homework Statement



A large pot of water is boiling on the stove. The pot has a heavy, close tting lid
which has a small hole to allow steam to escape, so that the lid does not lift up
from the pot. However, if too much steam is produced to escape through the hole,
the lid will lift to release the excess steam. The lid weighs 2 kg, and is 40 cm in
diameter. The hole for the steam to escape is 3 mm in diameter.

(a) Calculate the pressure that the steam in the pot would need to reach in order
to lift the lid.

(b) The steam exiting the hole forms a small jet as shown in Figure 8. Ignoring
viscosity eects and any small changes in height or density, show that the
maximum rate at which steam could escape from the hole before the excess
pressure lifts the lid is about 0.1 g s^{-1}
.I am not sure what equation to even use? Any help appreciated.

Should I be using Bernoulli's equation for part 'a'?
 
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  • #2
Part (a) asks what pressure is required to lift the lid. You've got the lid weight and its surface area (via its diameter). Do the obvious...

Part (b) may be where Bernoulli comes in. You'll want to look up the density of steam at normal atmospheric pressure.
 

1. How do I calculate pressure?

Pressure is calculated by dividing the force acting on an object by its surface area. The formula for pressure is P = F/A, where P is pressure, F is force, and A is surface area. Pressure is typically measured in units of Pascals (Pa) or Newtons per square meter (N/m^2).

2. What is the difference between gauge pressure and absolute pressure?

Gauge pressure is the pressure measured relative to atmospheric pressure. It is typically used to measure pressure in everyday applications. Absolute pressure, on the other hand, is the total pressure including atmospheric pressure. It is commonly used in scientific and industrial settings.

3. How does temperature affect pressure?

In general, as temperature increases, pressure also increases. This is because as particles in a gas gain more energy and move faster, they collide with each other and the container walls more frequently and with greater force, resulting in higher pressure. However, this relationship is not always linear and can vary depending on the gas and its properties.

4. What is the ideal gas law and how is it used to calculate pressure?

The ideal gas law is a combination of three gas laws: Boyle's law, Charles's law, and Avogadro's law. It states that for an ideal gas (one with no volume and no intermolecular forces), the pressure, volume, and temperature are related by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. This equation can be rearranged to solve for pressure, P = (nRT)/V.

5. Can pressure be converted to other units?

Yes, pressure can be converted to other units depending on the specific unit system being used. For example, 1 atmosphere (atm) is equivalent to 101,325 Pascals (Pa), 760 millimeters of mercury (mmHg), or 14.7 pounds per square inch (psi). It is important to always double check conversion factors and unit conversions to ensure accurate calculations.

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