# Force of water out of a hose

• zaguar
In summary, the question is asking for the force that a fireman must exert to keep a hose steady. The hose has a nozzle with an area of 5cm^2 and a cross sectional area of 360cm^2. It ejects water at a speed of 25m/s and a rate of 12L/s. To find the force, the mass flow rate of the water must be calculated, which is dependent on the cross section and velocity of the water. The difference in momentum entering and leaving the hose can then be used to find the force, which is equivalent to 296N in the direction of the water flow.
zaguar
The question states: A firemans hose has a nozzle of area 5cm^2 and the hose has a cross sectional area of 360cm^2. The hose ejects water at 25m/s and at a rate of 12L/s What is the force that the fireman must exert to keep the hose steady?

My attempt:

What I have done so far is to calculate the speed of water as it travels through the parts of the hose.

In the nozzle it travels at 24m/s (12000/500) and in the hose it is traveling at (12000/36000) = 0.33ms^-1, and as it is ejected, it is traveling at 25m/s.

So it goes from traveling at 0.33m/s to 24m/s to 25m/s. Hence, the force is
m(v-u)/t = 12kg/s * (25-0.33) = 296N​

So the fireman exerts a force of 296N in the direction of the flow of water.

Is this correct? It seems to simplistic to ignore the 24m/s in the nozzle, yet it seems to work.

Last edited:
This question is to do with momentum. Try and use the conservation of momentum to find the force the firefighter must exert on the hose to steady himself. You know the volume of water being ejected so its easy to find the mass. Also think of the time dependence of the mass.

Sorry, but I don't understand what you're getting at. What was wrong with the original approach?

zaguar said:
Sorry, but I don't understand what you're getting at. What was wrong with the original approach?

How is m=12kg/s?
The mass flow rate will depend on the cross section of the hose and the velocity. So, it won't be constant.

More specifically $$\dot{m} = \rho A v$$, where $$\dot{m}$$ is the mass flow rate.

What Kurdt says, is to find the difference in the momentum entering and leaving the hose. You can find the force from that.

Last edited:
Isn't that what I did?

Isn't the flow rate always going at 12L/s and the velocity changing, so that there is always 12 litres of water going through the pipe per second, but the speed is different in different parts of the pipe?

So the water is traveling at 0.33m/s in the hose, and exiting at 25m/s. If it is doing that, F=(mv-mu)/t=12*(25-0.33)=296N

## 1. How does the force of water out of a hose work?

The force of water out of a hose is created by the pressure difference between the water inside the hose and the surrounding environment. When the hose is turned on, the water inside is under high pressure and is forced out through the opening of the hose, creating a powerful stream of water.

## 2. Does the diameter of the hose affect the force of water?

Yes, the diameter of the hose does affect the force of water. A wider hose allows for more water to flow through, resulting in a stronger force. This is why fire hoses, which need to have a strong force of water, have a larger diameter than regular garden hoses.

## 3. Can the force of water out of a hose be increased?

Yes, the force of water out of a hose can be increased by adjusting the water pressure. The higher the water pressure, the greater the force of water. However, it is important to note that increasing the water pressure too much can damage the hose or the object being sprayed.

## 4. What factors can affect the force of water out of a hose?

The force of water out of a hose can be affected by several factors, including the water pressure, the diameter of the hose, the length of the hose, and any obstructions or kinks in the hose. These factors all play a role in determining the strength of the force of water coming out of the hose.

## 5. Is the force of water out of a hose consistent?

No, the force of water out of a hose is not always consistent. As the water flows through the hose, there may be changes in pressure due to factors such as friction or changes in the water supply. Additionally, the force of water may decrease as the water travels further from the source due to gravity and other forces.

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