**A&Q about 350Z**

Q:

Q:

a single-cylinder vertical atmospheric engine with bore=1.2m and a piston of 2700 kg mass is use to lift a weight. pressure in the cylinder after combustion and cooling is 22 kpa, while the ambient pressure is 98kpz.

assume piston motion is frictionless.

calculate:

1- mass that can be lifted if the vacuum is at the top of the cylinder and the piston moves up.

2- mass that can be lifted if the vacuum isat the bottom of the cylinder and the piston moves down.

**A:**

Am I doing your homework for you ?

I don't understand the question... too many variables. First the question gives information about 22kpa pressure, then asks how much the vacuum can lift. and what's the deal with "if the piston is at the TOP and then goes UP."? That can't happen.

I'm lost.

**A:**

1) 4

2) I got that rash from an Indonesian hooker also.

**A:**

It is just a piston-cylinder (not necessarily an IC engine) with two different cylinder pressures above and below the piston. Keeping in mind that the high pressure always wants to move towards the low pressure (unless work is being done on the system).

In case one the pressure above the piston is 22 kPa, and the pressure below is 98 kPa. So in case one the piston will move upwards.

In case two the pressures above the piston is 98 kPa and the pressure below the piston is 22 kPA. So the piston will move downwards.

I am assuming this is a lazy student post, but since I responded to Curtis I might as well provide a solution.

__ANSWER__

You only need two equations:

- Pressure = Force / Area
- Force = Mass * Acceleration

You are given pressure and area, so using the first equation you can find force. Note, since you have two pressures you just use the difference between the pressures.

( 98 kPa – 22 kPa ) / ( pi * ( 1.2 m / 2 ) ^ 2 ) = 86 kN

Now that you have force you can find mass. However, you have to assume the value of acceleration since it is not given. You also have to assume which direction gravity is acting. I am assuming gravity is 10 m/s² and acting downwards.

( 86 kN) / 10 m/s² = 8600 kg

This is the

**total**mass that can be support by the pressure. Since the pressure also supports the mass of the piston, you must subtract 2700 kg.

*Answer to case one is: 5900 kg (with g = 10 m/s)*

You can choose any value of “g” you want. You get more interesting answers if you choose 0 m/s² or ~31.84 m/s².

The answer to two may or may not be obvious. If it is not obvious, think about the solution to the first case. The limit to the mass is driven by the what value you choose for acceleration. This is because gravity is acting in the opposite direction of the pressure. However, in the second case both gravity and pressure will be acting in the same direction. The result is that there is no limit to the problem.

*Answer to case two: Infinite mass*

**A:**

am really gratefulllllll....

well no its not a lazy student..

but ideas are kind of mixed up...

THANKS A LOT...

**A:**

Well if that is the case then I apologize for being rude. Hopefully, the solution and not just the answer are useful for you.

**A:**

its ok.. dont worry..

and thanks again for helping..

i was not sure of being able to apply this here..

and i was also uncertain about the pressure thing..

**A:**

i didnt understand this part..

some people said its not true..

i should find the real mass in kg...

**A:**

You are given two pressures, one above the piston the other below, and no other information about the system. Unless more is known you can only assume that the pressures are constant and not changing.

However, in a more real world problem you would have a volume above and below the piston as well as pressure. As the piston moved the volumes would change, and when the volume changes the pressure must change. For a simple system the following equation would apply:

P_1 / V_1 = P_2 / V_2

So in case two as the piston moves downwards the volume below the piston decreases and the volume above the piston increases. As a result, the pressure below the piston increases and the pressure above the piston decreases. The piston will move downwards until the difference in pressure offsets the load of piston mass.

If you assume the pressure is constant, as I did, then there will always be a difference in pressure acting downwards. The only way to prevent the piston from moving downwards is with an upward acting force. Since I assumed gravity was acting downwards then there is no upward acting force, and the piston will move downward regards of the mass chosen.

**A:**

i guess you meant P_1 x V_1 = P_2 x V_2..

...

so infinte mass???

**A:**

You are correct, sorry about that.

Do what I mean, not what I say