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## Homework Statement

A student siphons water over a 8.5 m high wall at sea level. She then climbs to the summit of a mountain (elevation 4390 m , atmospheric pressure =58.5 kPa) and attempts the same experiment. Comment on her prospects for success.

## Homework Equations

Bernoulli's equation: ##P/\rho + v^2/2 + zg = C##

##\rho## -density of water

##P## - pressure

##v## -velocity

##z## -elevation

##g## -acceleration due to gravity

##C## - constant

## The Attempt at a Solution

I guess in order to find out whether the experiment works we need to find the maximum height over which water can be siphoned, this height depends on the pressure inside the pipe at the top most point ( my guess) and whether it is below or above the vapor pressure of water, if it is below the vapor pressure cavitation will occur and stop the flow right ?

Consider one end of the pipe as point 1 and the other end as point 2 ,now point 3 is in the middle part of the pipe that will be lifted to the maximum height.

Applying Bernoulli's equation between point 2 and 3

##P_2/\rho +v_2^2/2+ z_2g =P_3/\rho + v_3^2/2 +z_3g ##

##v_2 = v_3 ## since the pipe is of constant cross-section

##z_2 =0 ## as it is at sea level

##P_2=## atmospheric pressure at sea level

##P_3## is the pressure in the pipe at top most point = 58.5kPa correct ???

##z_3## is the maximum height to which the middle part of the pipe is elevated (=4390m correct ??)

assuming density to be constant , do i really need this ? should i just check whether the pressure at point 3 is above or below the vapour pressure of water and decide whether the experiment will work ?

I need to find the vapour pressure of water which according to wikipedia depends on temperature

https://en.wikipedia.org/wiki/Vapour_pressure_of_water

##P\text{ (mmHg)} = \exp\left(20.438 - \frac{5044}{T\text{ (K)}}\right) ##

Taking temperature as 260.77K based on altitude

http://www.engineeringtoolbox.com/air-altitude-temperature-d_461.html

, i get P =399.125 Pa as vapour pressure is that correct ?

does this mean water will not cavitate ? as the pressure at the altitude of 4390 m is 58.5kPa (> 0.399 kPa )

So the student's experiment will work ?

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