Calculating Initial Velocity of Water After Nozzle Increase

In summary, to determine the increase in velocity of water through a nozzle, you can use the calculations given in Example 5-1 and compare the ratios of the hose diameter and nozzle diameter, as well as their cross-sectional areas. This will give you an estimation of the increase in linear speed, which in this case is 6.25 times, not exactly 6 times.
  • #1
goldfish9776
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Homework Statement


how to know that the nozzle increases the velocity of water by 6 times? it's not given ... and no data for initial velocty given

Homework Equations

The Attempt at a Solution

 

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  • #2
goldfish9776 said:

Homework Statement


how to know that the nozzle increases the velocity of water by 6 times? it's not given ... and no data for initial velocty given

Homework Equations

The Attempt at a Solution

Did you look at the start of the problem calculations given in Example 5-1 at the bottom of the first image?

That's the one where the hose is being used to fill a bucket of a certain size in a certain amount of time. You can work out the velocity of the flow from the information given in the example. The second image just sums up the calculations from the first image.
 
  • #3
SteamKing said:
Did you look at the start of the problem calculations given in Example 5-1 at the bottom of the first image?

That's the one where the hose is being used to fill a bucket of a certain size in a certain amount of time. You can work out the velocity of the flow from the information given in the example. The second image just sums up the calculations from the first image.
yes, but i still can't understand the velocity increases by 6 times...
 
  • #4
goldfish9776 said:
yes, but i still can't understand the velocity increases by 6 times...
What is the ratio between the hose diameter and the nozzle diameter?
What is the ratio of their cross-sectional areas?
Since the volume flow rate must be the same for both, what does that tell you about the ratio of the linear speeds?
 
  • #5
goldfish9776 said:
yes, but i still can't understand the velocity increases by 6 times...
You've got a nozzle on the end of the hose. The water flowing through the hose is incompressible, so whatever amount goes in one end of the hose must come out the other end, in the same amount of time. You are also given the diameter of the hose and the diameter of the exit of the nozzle.

The flow rate through the hose Q = Area of the hose × velocity of the water. Since Qin = Qout and you can calculate Ain and Aout for the hose given the indicated sizes, then the only thing which remains is to calculate Vin and Vout. You are told how long it takes to fill a bucket with a certain volume of water, and this gives you Qin.
 
  • #6
haruspex said:
What is the ratio between the hose diameter and the nozzle diameter?
What is the ratio of their cross-sectional areas?
Since the volume flow rate must be the same for both, what does that tell you about the ratio of the linear speeds?
2 /0.8 = 2.5
1 / (0.4^2) = 6.25
so , the ans is It's 6.25 times , not 6 times?
 
  • #7
goldfish9776 said:
2 /0.8 = 2.5
1 / (0.4^2) = 6.25
so , the ans is It's 6.25 times , not 6 times?
Yes. I don't think they intended the 6 to be exact.
 
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1. How do you calculate initial velocity of water after a nozzle increase?

The formula for calculating initial velocity of water after a nozzle increase is v = (2gh)^1/2, where v is the initial velocity, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the water column.

2. What is the significance of calculating initial velocity of water after a nozzle increase?

Calculating the initial velocity of water after a nozzle increase is important in understanding the flow rate and pressure of a fluid system. It can also help determine the efficiency of a nozzle and can be used in designing and optimizing fluid systems.

3. How does the size of the nozzle affect the initial velocity of water?

The size of the nozzle has a direct impact on the initial velocity of water. A smaller nozzle will result in a higher initial velocity, while a larger nozzle will result in a lower initial velocity. This is because a smaller nozzle creates a narrower stream of water, increasing the velocity of the water as it exits the nozzle.

4. Can the initial velocity of water after a nozzle increase be greater than the speed of sound?

No, the initial velocity of water after a nozzle increase cannot be greater than the speed of sound. The speed of sound in water is approximately 1482 m/s, and the formula for calculating initial velocity of water after a nozzle increase only applies to subsonic flows.

5. How can the initial velocity of water after a nozzle increase be measured in a real-world scenario?

The initial velocity of water after a nozzle increase can be measured using various instruments such as Pitot tubes, flow meters, or by measuring the distance and time it takes for the water to travel a certain distance. It is important to consider factors such as friction and turbulence in the measurement process to get an accurate result.

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