# Thermodynamics, work interaction, pressure, power

1. Jan 14, 2012

### xzibition8612

1. The problem statement, all variables and given/known data
Denver's Mile High football stadium incorporates a system by which a section of stands can be moved to accommodate different sports on the field. The grandstand, which has a mass of 4x10^6 kg, can be moved a distance of 45 m on a thin film of water. The movable grandstand rests on 46 bearing pads that are each 1.22m in diameter. Water at high pressure is pumped into each of the pads until the stands are lifted a vertical distance of 3.8 cm. Excess water forms a lubricating film over which the grandstand is moved. The force required to move the stands is approximately 4.45 N per 450 kg of staduym mass. Calculate the following:

a. The pressure of the water under each bearing pad

b. The power of the motor required to move the grandstands over the distance of 45 m if the job takes 1 h.

c. the work required to raise the grandstand 3.8 cm.

2. Relevant equations

See attachment formulas. Here is a brief description of each:
1. Force-displacement work
2. Force-displacement power
3. PdV work (piston)
4. PdV power

3. The attempt at a solution
Am I picturing this problem correctly (see "picture" attachment)?
I don't understand the bearing pads part. Do the bearing pads move or are the bearing pads wet and the grandstand slides on the bearing pads? And for part (a) asking the pressure of the water under each bearing pad, does this mean the water pressure inside each pad? I'm very confused about this problem and don't even know where to start. Any help would be appreciated. Thanks!

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2. Jan 14, 2012

### Redbelly98

Staff Emeritus
Equations 1 & 3 are correct, but 2 & 4 are not.
For #2, recall that W = F·d, where d is the displacement.

I'm also not clear on whether the bearing pads move or are stationary, but I think that's not necessary for answering the questions. Yes, they would mean the water pressure inside each pad. Each pad is acting as a hydraulic lift, similar to in this picture:

To help get you started: how much force must each bearing pad exert on the grandstand in order to lift it?

3. Jan 14, 2012

### xzibition8612

For (a), P= density x gravity x height

So P = 1000 kg/m^3 x 9.8 m/s^2 x 0.032 m
P = 313.6 N/m^2

(b) Power (my equation 2):

Power = F x V (V=velocity)
Since 4.45N is required to move 450 kg, then (4x10^6 kg / 450 kg) x 4.45 N = 39555 N = F
Velocity = 45m/60s
Power = F x V = 39555 N x 0.75 m/s
Power = 29666.25 N-m/s

(c) Use equation 1.
Integrate from 0 to 3.8 cm. Only need to find F, so would that be my answer in (a) 313.6 N/m^2?
So work would then be 11.9 N/m....but the units are not of energy, so it's wrong. Don't know how to go on.

I think the 46 bearing pads can be treated as one single pad, as the effect is the same. Also the 1.22m diameter is extra unnecessary information right?

Last edited: Jan 14, 2012
4. Jan 14, 2012

### Redbelly98

Staff Emeritus
Not quite. That is the change in water pressure over a depth of 0.032 m.

I will repeat my earlier hint: how much force must one bearing pad exert in supporting the 4*106 kg grandstand?
Your method is correct, but note that it takes 1 hour to move it. How many seconds is that?
This is where you went wrong, since a force must have units of N, so that can't be the force.

So, how much force is required to lift an object of mass 4x106 kg?

5. Jan 14, 2012

### xzibition8612

How much force...so F=ma, thus Force = 4x10^6 kg x 9.8 m/s^2
Force = 3.92x10^7 N. This much force is needed to lift the grandstand. Yes so this number would be used in part (c) as F.

As for (a), P=F/A, and we know it's a circular bearing pad with diameter 1.22, thus radius is 0.61m, which means each pad has an area of 1.169 m^2 which is A. There are 46 pads, and it's asking for the water pressure under *each* pad, so I have to divide 3.92x10^7 N by 46 which yields 8.5x10^5 N, thus my answer is 7442 N/m^2.

I think this is correct? And only for part (a) do I have to consider 46 pads, whereas in parts (b) and (c) I can treat the bearing pads as one single pad right?
And 3600 seconds in 1 hour : )
Thanks a lot for your help.

Last edited: Jan 14, 2012
6. Jan 15, 2012

### Redbelly98

Staff Emeritus
You're good up to here
Oops. Arithmetic error? Did you use the 1.169 m^2 area to get this?
You're correct that for (b) and (c) you just need to consider the total force. Note that in (b) the pads are irrelevant, since it is a single separate motor that moves the grandstand horizontally -- the pads are only used to lift the grandstand vertically.

Yup!
You're welcome.

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