Question

 The highest that George can suck water up a very long straw is 2.0 m. (This is a typical value.) What is the lowest pressure that he can maintain in his mouth?

Answer 1

Concepts and reason

Use the concept of change of pressure to solve this problem.

Initially, calculate the pressure applied by George to suck the water by using the relation between the pressure, density, height, and acceleration due to gravity.

Later, find the lowest pressure that George can maintain at his mouth by using the relation between change in pressure, atmospheric pressure, and the pressure applied by George.

Fundamentals

The force that is acting on the surface area in the perpendicular direction is called as pressure. It is simply the force per unit area.

It is denoted with P. its units are Pascal’s (Pa).

The formula for the change of pressure is as follows:

$\Delta P=P^{atm}-P$ …… (1)

Here, $\Delta P$ is the change in the pressure, P is the pressure, and $P^{atm}$ is the atmospheric pressure.

The formula for the pressure is as follows:

$P=\rho gh$ …… (2)

Here, $\rho$ is the density of the water, g is the acceleration due to gravity, and h is the height of the straw.

The pressure applied by George is,

$P=\rho gh$

Substitute, $1000\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ for $\rho$ , $9.8\mathrm{m}/{\mathrm{s}}^2$ for g, and 2.0 m for h

$\begin{array}{c}P=\left(1000\mathrm{k}\mathrm{g}/{\mathrm{m}}^3\right)\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)\left(2.0\mathrm{m}\right)\\ =19600\mathrm{P}\mathrm{a}\end{array}$

The lowest pressure that George can maintain at his mouth is,

$\Delta P=P^{atm}-P$

Substitute $\left(1.013\times {10}^5\mathrm{P}\mathrm{a}\right)$ for $P^{atm}$ , and 19600 Pa for P

$\begin{array}{c}\Delta P=\left(1.013\times {10}^5\mathrm{P}\mathrm{a}\right)-19600\mathrm{P}\mathrm{a}\\ =81700\mathrm{P}\mathrm{a}\\ \approx 82\mathrm{k}\mathrm{P}\mathrm{a}\end{array}$

Ans:

The lowest pressure that George can maintain at his mouth is 82 kPa.

Answer 2

14) Water has a density of 1 g / cm^3. So multiply by 2 meters (200 cm) and by earth's gravity (9.8 m/s^2), and you have a pressure exerted of 1.96×10^5 g / (cm s^2). That converts to 19.62 kPa (use google calc to convert if you want). Pressure exerted is the same as negative pressure required to keep it up. So george can get -19.62 kPa or 19.62 kPa below atmospheric pressure, so that's 101.33 - 19.62 = 81.71 kPa is the lowest pressure he can hold. (or in Pa, it is 8.2 * 10^4 Pa)

Answer 3

According to Bernoulli's principle,

Pressure energy = Gravitational energy

assuming pressure at surface of water is equal to atmospheric pressure

The pressure inside mouth should be smaller than the atmospheric pressure by 19600 Pa.