Manometer -- determine height from relative pressure

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The discussion centers on calculating height using a manometer and relative pressure. A participant asserts that the correct height is 5.6 meters but is uncertain about their calculations. There is confusion regarding the equations used, specifically the relationship between gauge pressure and absolute pressure. One participant questions the accuracy of the initial equation presented, suggesting an alternative formulation. The conversation highlights the importance of correctly applying pressure equations in fluid mechanics.
daphnelee-mh
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Homework Statement
A Burdon gauge is mounted on the top of the vessel at point M . The relative pressure at M is -980Pa, determine h1 if H=1.5m, h2=0.2m
Relevant Equations
Pm=Pa- Pmabs
The correct answer is 5.6m, not sure where I made the mistake.
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##P_{M gauge}=P_{atm}-P_{M abs}##?
Doesn't look right to me.
 
I get ##P_{Mabs}=p_{atm}+P_M##
 
Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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