The pressure in a fire hose is 20 atm. How high can a firefighter spray water from this hose?

One atm is about 1×105 Pa. The density of water is 1.0 g/ml, or 103 kg/m3. The acceleration of gravity, g, is 9.8 m/s2.

To determine the height that a firefighter can spray water from the hose, we can use the principles of fluid mechanics and Bernoulli's equation.

First, let's convert the pressure from atm to pascals (Pa) using the conversion provided.

20 atm = 20 x 1x10^5 Pa = 2x10^6 Pa

Now, to find the height that the water can be sprayed, we can use Bernoulli's equation, which states that the total pressure in a fluid system is constant along a streamline.

In this case, we can consider two points: the location where the water is sprayed (point 1) and the height at which the water reaches (point 2). At point 1, the pressure is the initial pressure in the hose (2x10^6 Pa) and at point 2, the pressure is atmospheric pressure (1x10^5 Pa).

Using Bernoulli's equation:

P1 + 1/2 * ρ * v1^2 + ρ * g * h1 = P2 + 1/2 * ρ * v2^2 + ρ * g * h2

Where:
P1 and P2 are the pressures at points 1 and 2 respectively,
ρ is the density of water (103 kg/m^3),
v1 and v2 are the velocities of the water at points 1 and 2 (which we assume to be negligible in this case),
g is the acceleration due to gravity (9.8 m/s^2),
h1 is the initial height (0 m, as the water is sprayed horizontally),
and h2 is the height we want to find.

Since the water is sprayed horizontally, the velocity term (v1^2 and v2^2) can be considered negligible compared to the pressure terms.

P1 + ρ * g * h1 = P2 + ρ * g * h2

Substituting the given values:

2x10^6 + 103 * 9.8 * 0 = 1x10^5 + 103 * 9.8 * h2

2x10^6 = 1x10^5 + 103 * 9.8 * h2

Rearranging the equation:

103 * 9.8 * h2 = (2x10^6 - 1x10^5)

h2 = (2x10^6 - 1x10^5) / (103 * 9.8)

h2 = 1948.97 m

Therefore, the firefighter can spray water up to approximately 1948.97 meters high using a hose with a pressure of 20 atm.