# Maximum height for water from a fire hose

• tuki
In summary, the conversation discusses the problem of determining the maximum height that water can reach when flowing through a fire hose with a diameter of 4.0 cm and a flow rate of 10 L/s, and a pressure of 2.2 bar inside the hose. The water density is given as 1.00E3 kg/m^3 and the air pressure outside the hose is 1.0 bar. The attempt at a solution involves calculating the speed of the water particle as it exits the hose and then using a function to determine the maximum height, which gives a result of 1.6 m. However, the correct answer is given as 26 m, which leads to the suggestion of using Bernoulli's equation
tuki

## Homework Statement

Fire hose has diameter of 4.0 cm and flow rate of 10 L/s. There is pressure of 2.2 bar inside the hose. How high the water can go at best? Water density is 1.00E3 kg/m^3 and air pressure outside the hose is 1.0 bar.

## Homework Equations

Flow rate
$$Q = Av$$
Newtons equations?

## The Attempt at a Solution

I tired to find speed for water particle when it exits the hose. I can get speed directly from flow rate.

$$v = \frac{Q}{A} = \frac{Q}{(\frac{d}{2})^2 \pi}$$
$$v \approx 7.957 \text{ m/s}$$

If we would aim the hose at 45 angle it would follow height as function of time as:

$$h(t) = vt-gt^2$$

i solved the maxima with first derivative $$t = \frac{v}{2g} \approx 0.4055 \text{ s}$$

then you would compute the height from the function $$h(0.41\text{ s}) \approx 1.6 \text{ m}$$

However the correct answer should be 26m. What I'am doing wrong?

Try Bernoulli's equation and don't forget the necessary unit conversions.

hoses have nozzles to convert pressure to speed
kuru was faster to point you in the right direction
note they ask for maximum height, so I d aim a little higher

BvU said:
hoses have nozzles to convert pressure to speed
kuru was faster to point you in the right direction
note they ask for maximum height, so I d aim a little higher
kuruman said:
Try Bernoulli's equation and don't forget the necessary unit conversions.

I tried Bernoulli's equation and ended up with this.
$$p_1 + \frac{1}{2}pv^2_1 = p_2 + \frac{1}{2}pv_2^2$$
Speed can be expressed as
$$v = \frac{Q}{\pi (\frac{d}{2})^2}$$
$$\implies v_2 = \sqrt{\frac{p_1-p_2}{\rho}+(\frac{Q}{(\frac{d}{2})}^2 \pi)^2\cdot 2}$$
when i compute with numbers i get 19m/s for speed.

Computing maximum height with mgh = 1/2 mv² we get that h = v²/2g, which gives approx 18.3 m.
Correct answer was 26 m. Any suggestion on what I'am doing wrong?

Since the problem is asking for the speed, use Bernoulli's equation between a point just inside the hose and the point at maximum height. You don't really need the speed. Also, I get 26 m if I assume that the pressure outside is zero. It looks like there is an error in the quoted answer that needs to be checked.

Last edited:
BvU

## 1. What factors affect the maximum height for water from a fire hose?

The maximum height for water from a fire hose is affected by several factors, including the pressure of the water, the diameter of the hose, and the angle at which the hose is held.

## 2. Is there a standard maximum height for water from a fire hose?

There is no standard maximum height for water from a fire hose, as it can vary depending on the type of hose, the water pressure, and other factors.

## 3. Can the maximum height for water from a fire hose be increased?

Yes, the maximum height for water from a fire hose can be increased by increasing the water pressure, using a larger diameter hose, or holding the hose at a steeper angle.

## 4. How does the maximum height for water from a fire hose impact firefighting efforts?

The maximum height for water from a fire hose can impact firefighting efforts by determining the reach of the water and the effectiveness of extinguishing the fire. In some cases, it may be necessary to use additional equipment or techniques to reach higher areas.

## 5. Is there a way to calculate the maximum height for water from a fire hose?

There are various equations and formulas that can be used to estimate the maximum height for water from a fire hose, but it is important to keep in mind that the actual height may vary depending on real-world conditions and variables.

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