To suck water up a straw to a maximum height of 187 mm, what minimum gauge pressure must be produced in the lungs? Note that in order to be able to suck up water, the pressure in the lungs must be lower than the pressure outside by the exact amount of pressure created by the weight of the column of water in the straw.
Gauge pressure is the pressure relative to the ambient atmospheric pressure.
A pascal (Pa) is the unit of measurement of pressure equivalent to 1 N (newton) acting on an area of 1 m².
To produce a pressure sufficient to suck water to a height of 187 mm, the pressure is equivalent to the total weight of 187 mm high of water in a container exactly 1 m³ in area.
Let g=acceleration due to gravity, m/s²
Pressure = mg N
=(0.187*1*1) m³ * 1000 kg/m³ * 9.8 m/s²
= 18326 pascals
= 18.326 KPa
Since to suck water, the pressure must be negative, so the required gauge pressure is -18.3 KPa.
Sorry, the numerical value was erred by a factor of 10. It should read:
= 1833 pascals
= 1.83 KPa
To determine the minimum gauge pressure required in the lungs to suck up water to a maximum height of 187 mm in a straw, we need to consider the concept of pressure difference.
The pressure difference needed to lift a column of liquid in a straw is equal to the weight of that column of liquid. In this case, the weight of the column of water in the straw is the force exerted due to gravity on the water mass.
To calculate the pressure difference, we can use the equation:
ΔP = ρgh
where:
ΔP is the pressure difference,
ρ is the density of the liquid (water),
g is the acceleration due to gravity,
and h is the height of the column of liquid (187 mm).
Firstly, we need to convert the height from millimeters to meters:
h = 187 mm = 187/1000 = 0.187 m
The density of water is approximately 1000 kg/m^3, and the acceleration due to gravity is 9.8 m/s^2.
Substituting these values into the equation:
ΔP = (1000 kg/m^3)(9.8 m/s^2)(0.187 m)
Simplifying the expression:
ΔP = 1838 Pa
Therefore, the minimum gauge pressure that must be produced in the lungs is 1838 Pascal (Pa) to lift the water up to a maximum height of 187 mm in the straw.