Suppose a meteorologist, in an effort to be more environmentally and safety-cons

Question

Suppose a meteorologist, in an effort to be more environmentally and safety-conscious, chose to measure atmospheric pressure using a barometer filled with water instead of mercury. What would be the measured height of water if, on that day and location, a mercury barometer had a height of 758 mm Hg?

Let the density of water be 0.997 g/cm^3, the density of mercury be 13.580 g/cm^3, and g = 9.81 m/s^2.

Do not assume that the pressure at the top of the water manometer is zero, but can be assumed to be zero for the mercury manometer.

Consider that the top volume be full of water vapor (which much therefore be in equilibrium with the top surface of the water liquid). Assume the temperature that day is 28.1°C.

Explanation / Answer

Solution-

Given;

P = 758 mm Hg

Density of water (dH2O) = 0.997 g/cm^3

Density of mercury (d Hg) = 13.580 g/cm^3

g = 9.81 m/s^2.

H =?

We know the equation

P = F/A                        

Here Force = m * g   = d*A*h*g                                     (Mass = d*A*h)

P = (d*A*h*g)/A                           [A = Area, d =density, h =height ]

P = d*h*g

h = p/d*g

Insert the value in equation

h = (758 mm Hg)/( 0.997 g/cm^3*9.81 m/s^2.)

h = 77.50mm

Answer- Measured height of water = 77.50mm

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