- What is the lowest pressure he can maintain in his mouth?
In this question, we have to find the minimum pressure that George can maintain in his mouth while he sucks water from a 2.0 m straw.
To solve this question, we should recall our concept of Pressure and Hydrostatic Pressure. So what is Pressure? It is defined as “The force on the unit area of an object.” The unit of pressure is Pascal $ (Pa)$. Pressure is a scalar quantity having magnitude but no direction.
The different types of pressure are Atmospheric, Absolute, Differential, and Gauge pressure.
To understand the concept of hydrostatic pressure, imagine there is a container with water in it, and at every point inside the container, pressure exists on the liquid as there is liquid above it. So this existing pressure is known as hydrostatic pressure, and it is directly proportional to the depth of the liquid. Thus we can say that as the depth of the point increases, the hydrostatic pressure also increases.
Expert Answer
It is given that there is a person sucking the liquid from the straw and the highest that he sucks the liquid up is 2.0 m. Our required pressure is the pressure that is built inside the straw.
Height of water $ h = 2.0 m $
Let Atmospheric pressure = $ P_o$
Min pressure that can be maintained = $ P $
Pressure of water column = $P_o $ – $ P$
We know that
\[P_o = 1.013 \times {10}^5 {N}{/m^2}\]
Hydrostatic pressure =$ \rho gh$
Here,
$\rho$ = Density of the fluid.
$g$ = Acceleration of gravity
$h$ = Depth of the fluid
Then we have,
\[ P_o − P = \rho gh \]
So the required pressure that should be made by the person is equal to the atmospheric pressure outside of that straw minus the hydrostatic pressure.
\[ P = P_o − \rho g h\]
Here we have
Density of water $\rho =1000 \\{ kg }/{ m^3 }$ and $ g= 9.81 $
Putting values in above equation, we get:
\[ P=1.013\times{ 10 }^5- 1000\times9.81\times2\]
\[ P=\ \frac{ 8.168\ \times{ 10 }^4}{ 1.013 \times{ 10 }^5 }\]
Numerical Results
By solving the equation above, we will get the required pressure to be made, which is as follows:
\[ P= 8.168 \times { 10 }^4 { N }/{ m^2}\]
Thus the minimum pressure that George can maintain in his mouth while he sucks water from the long straw to the height of $2.0 m$ is as follows:
\[P=0.806\ atm\]
Example
A person sucks liquid from a straw to the height of $3.5m$. What will be the lowest pressure that he can keep in his mouth in $N/m^2$?
Person sucking the liquid from the straw: the maximum height achieved by the liquid is equal to $3.5 m$.
Height of liquid $h=3.5m$
\[P=P_o − \rho gh\]
Putting values in above equation, we get:
\[P=1.013\times{10}^5-1000\times9.81\times3.5\]
\[P=8.168 \times {10}^4 {N}/{m^2}\]