Magnitude of the rate of change of momentum of water

In summary, the problem involves finding the rate of change of momentum of water being sprayed from a fire hose at a burning building. The first part asks for the magnitude of the rate of change, which can be found by converting the given amount of water into mass and multiplying it by the velocity. The second part concludes that the rate of change of momentum is negative. The third part involves finding the force exerted by the water in a given amount of time. However, there may be an issue with the conversion from gallons to kilograms, as the given answers have been incorrect.
  • #1
JadeBunny
3
0
Rate of change of momentum

Homework Statement



Hey everybody this is my first post and I really hope you guys can help me out. Ok so here's the problem which is divided into three parts:

The first part consists of this: A fire hose sends 1464 gallons of water perminutre against a burning building at 92 m/s and does not bounce back. What is the magnitude of the rate of change of momentum of the water. Answer in Newtons.

The second part which I've figured out asks whether the rate of change of momentum of the water cannot be determined, is positive or negative. The answer is that it's going to be negative.

The third part consists of finding the once exerted by the water in 1.7 minutes.

Homework Equations


I know thus far that momentum or delta p = mass x velocity


The Attempt at a Solution



So far I've tried converting the amount of water given into a mass given that the density of water is 1kg/L which gave me a value of 3.786 kg/gal which I used with 1 min= 60 sec to convert the gal/min value into 92.38 kg/sec

I multiplied this by the velocity given (vf-vi= -92) and got a value of -8498.8 N, which when I inputted into the online homework program said was incorrect.

I've been working on this for several hours now and am currently stuck at this moment. The assignment is actually due the 23rd but the answers need to be submitted well before then. Any insight anybody could give me would be greatly appreciated. Thanks!
 
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  • #2
I'm getting the same answer as you... I suspect the problem is with the conversion from gallons to kg... I'm trying to find the conversion...
 
  • #3
maybe use 3.78541178 kg/gallon ? changes the last few decimal places...

these are US units right? not UK units I'm guessing...
 
  • #4
well we've been using the metric system thus far. I'm suspecting that the conversion rate might be off but I've yet to be able to verify that.
 
  • #5
Did you enter -8498.8 N or 8498.8 N.

The first part asks for the magnitude, so you need to enter the positive value...
 
  • #6
Yes I put it in positive form and it's still wrong. The thing is the program the homework is on only let's you submit an answer a max of 7 times, thus far I've tried three answers and they've all been wrong. They were: -8498.81, 8497.49, -4726.54

My question now is are we sure this is the right way to convert to mass for the water and the velocities: our inital will be 92 right, so the initial I'm presuming is 0 but is that right?
 

FAQ: Magnitude of the rate of change of momentum of water

What is momentum of water?

Momentum of water is a measure of the mass and velocity of water in a given direction. It is calculated by multiplying the mass of the water by its velocity.

How is the rate of change of momentum of water calculated?

The rate of change of momentum of water is calculated by dividing the change in momentum by the change in time. This can also be expressed as the derivative of momentum with respect to time.

Why is the magnitude of the rate of change of momentum of water important?

The magnitude of the rate of change of momentum of water is important because it can help us understand the force and impact of water in various situations, such as in fluid dynamics or in hydraulic systems. It can also help us calculate the amount of energy that can be generated by water, such as in hydroelectric power plants.

How does the magnitude of the rate of change of momentum of water affect the environment?

The magnitude of the rate of change of momentum of water can have significant impacts on the environment. For example, strong and sudden changes in momentum can lead to erosion of river banks and changes in the flow of water, which can affect aquatic habitats. It can also cause flooding and damage to surrounding areas.

What are some real-world applications of studying the magnitude of the rate of change of momentum of water?

Studying the magnitude of the rate of change of momentum of water has many real-world applications, such as in predicting and mitigating the effects of floods and tsunamis, designing and maintaining efficient and safe hydraulic systems, and understanding the behavior of waves in oceans and rivers. It is also crucial in the development of renewable energy sources, such as hydroelectric power.

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