Question

Engineering wouldn't answer. Hopefully you mathematicians could help.

Solve this manometer problem...

MEK SG = 0.805, so density = 0.805 g/cm^3
Mercury SG = 13.546 so density = 13.456 g/cm^3

Answer 1

I assume you can get part (a) from the weight of the fluid.

Answer 2

I was thinking I might need to take the volume and multiply the density. The answer given is 15.63 psi

Answer 3

P(abs.) = P(atm) + (rho)(g)(h)

Answer 4

15.63 psi seems a little high. What did you use for P(atm) and what was the contribution from the liquid?

Answer 5

Never mind, I was off by a decimal point when I was converting from pascals to psi, 15.63 or 15.64 sounds right.

Answer 6

For part (b) if it is an open-end manometer, then if both ends were open to the atmosphere, then the level of mercury would be even in both sides of the tube, so the additional height above the d1=0 datum is only from the gauge pressure of the liquid in the tank. You can convert your psi measurement to mm Hg to find that.

Answer 7

can you help explain part a) I still havent gotten it to work.

Answer 8

what is teh "rho" you mentioned

Answer 9

Greek letter 'rho' is the usual symbol for density.

Answer 10

right ok. Thats what I am using. I'm going to first convert all my units and see if I can get the same answer. might take some time

Answer 11

We can take standard atmospheric pressure to be 14.7 psi.
Do you have all the conversion factors you need?

Answer 12

I got it!!!

Answer 13

Now b) i know the left side of teh manometer must equal the right side. so i think I setup an equation for that and solve for h

Answer 14

Mine came out to 15.6391 psi. How about you?

Answer 15

(Should be rounded to 15.6 psi due to significant figures, though)

Answer 16

15.634 same thing really

Answer 17

correct 3 sig digs

Answer 18

b) the answer given is 48.5 mm Hg

Answer 19

Yes, you could set up an equation to solve part (b), but I'm guessing the reasoning I provided will find it too. I'll check.

Answer 20

760 Hg = 14.696 psi (lb force/in^2)

Answer 21

I got 48.5657 which I'll round to 48.6 mm

Answer 22

No equation necessary, just convert the pressure of the liquid to mm Hg.

Answer 23

1 psi = 51.71 mm Hg

Answer 24

nice. I'm setting it up like \[P _{abs}+\rho gd _{1}= P _{atm}+\rho g h\]

Answer 25

is that what you did

Answer 26

Nope.

Answer 27

Scroll up to my 5th reply to see my reasoning.

Answer 28

That is the equation, but a lot of the terms drop out due to simplifying assumptions.

Answer 29

P(abs) includes P(atm) so you can subtract that from both sides.
It says to take d1=0 for simplicity, so that term's gone.
g cancels out on both sides.
You're left with a proportion of ratio of heights equal to a ratio of densities, but you don't need to calculate that either. You already know the pressure of the liquid.

Answer 30

I got it. gauge = abs - atm

Answer 31

so if d = 0 that term drops out and I am left with the above formula. I'm embarassed I didnt see it. thx

Answer 32

That's why I don't like to start with equations. I imagine the situation and develop the equation myself.

Do you know what to adjust for part (c)?

Answer 33

there is no atm pressure because it is now under vacuum. so gauge = atm

Answer 34

which is 760 mm Hg and that is the answer. Thanks for helping me work through it. I now have a better understanding.

Answer 35

You're very welcome. I love this stuff.