Why would prefer to use the mercury instead the water in a sphygmomanometer?

Answer 1

Because #1*atm# supports a column of mercury #760# #mm# high..........

But given the density of mercury compared to water (#rho_"Hg"=13.55*g*cm^-3; rho_"water"=1*g*cm^-3#, it would require a column of water approx. #10*m# high to support a pressure of #1*atm#.
Now sphygmomanometers take blood pressure measurements; typically we measure #50-60*mm# above or below atmospheric pressure. A measurement of a water column would still be prohibitively high.
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Answer 2

Because mercury has a lower vapor pressure and a higher density than water, it is a better choice for a sphygmomanometer because it can measure blood pressure more accurately with a shorter column and less chance of evaporation-related errors.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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