Bernoulli's equation limitations?

Click For Summary

Homework Help Overview

The discussion revolves around a problem involving fluid dynamics, specifically the application of Bernoulli's equation in the context of a firehose shooting water to a height of 35 meters. Participants explore the implications of nozzle diameter and pressure calculations based on given flow rates and velocities.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the required speed of water at the nozzle to reach the specified height and question the relevance of Bernoulli's equation in this context. There are attempts to apply the continuity equation and clarify the relationship between nozzle diameter and hose diameter. Some participants express confusion over negative pressure results and the physical implications of such values.

Discussion Status

The discussion is active, with participants sharing calculations and questioning assumptions. Some have reached agreement on the necessity of using the continuity equation, while others express skepticism about the problem's parameters and the resulting pressure calculations. There is no explicit consensus, but various interpretations and approaches are being explored.

Contextual Notes

Participants note potential discrepancies in the problem's setup, such as the relationship between nozzle and hose diameters, and the implications of negative pressure in fluid dynamics. There is an acknowledgment of the need for careful consideration of the physical principles involved.

madchemist
Messages
67
Reaction score
0
A firehose must be able to shoot water to the top of a building 35 m tall when aimed straight up. Water enters the hose at a steady rate of 0.500 m3 / s and shoots out of a round nozzle. (a) What is the maximum diameter this nozzle can have? (b) If the diameter of the hose is 10 cm, what is the pressure in the hose 1.00 m below the nozzle?

(Vyf)^2 = (Vyi)^2 + 2ay(yf-yi)
J = AV
A = (pie)r^2
P1 + 0.5pv1^2 + pgh1 = P2 + 0.5pv2^2 + pgh2

Found that maximum diameter in part (a) was 15.6 cm. This means the nozzle diameter is more than 50% larger than the hose diameter. When I applied Bernoulli's equation, I came up with a negative number for the pressure in part (b) like this... P1 = (1.01*10^5) + 500(26.19^2 - 63.66^2) + 9800 = -1572539.75 pa. I'm not sure how to explain it, but I think it has something to do with the fact that the water ejected from the narrow hose would remain at the same velocity, because the is no force causing it to conform to the larger dimensions of the nozzle. Therefore, the pressure would be simply Patm + pgh = 110800 pa?
 
Last edited:
Physics news on Phys.org
1. What speed MUST the water have at the nozzle in order to reach 35 m height?
The answer has nothing to do with Bernoulli's law.

2. What diameter of the nozzle will provide this speed?
Again, nothing to do with Bernoulli. (you'll get something definitely smaller than the diameter of the hose.)
Hint: continuity equation

3. For part b) you need to use Bernoulli's law.
 
nasu said:
1. What speed MUST the water have at the nozzle in order to reach 35 m height?
The answer has nothing to do with Bernoulli's law.

2. What diameter of the nozzle will provide this speed?
Again, nothing to do with Bernoulli. (you'll get something definitely smaller than the diameter of the hose.)
Hint: continuity equation

3. For part b) you need to use Bernoulli's law.

I agree to "1". I also agree to "2" that the continuity equation is useful here. I disagree however that the diameter of the nozzle is smaller than the diameter of the hose. I got 15.6 cm for the nozzle and 10 cm for the hose is given. I know it's a funny looking hose, but who am I to argue with the problem statement?
I agree to "3" but as previously stated, Bernoulli's law gives negative Pascals.
 
I got Vi = 26.19 m/s.
 
I've got the same value.
I think you are right, I did not do the complete calculation before.
Now I did the hole think and I get as you said, around 16 cm for diameter.
Sorry for your time.
It seems that the hose becomes larger at the nozzle (unless there is some mistake in the number for the flow rate).

If the water slows down in the nozzle, then the pressure should increase, compared to the region 1 m below where it flows faster (smaller diameter). It makes sense to have a negative difference.
 
But isn't there no such thing as NEGATIVE pressure? I think the water ejected from the hose would remain at the same velocity (I calculated it as 63.66 m/s) as it passed by the nozzle (assuming the nozzle isn't very long). In other words there would be no change in velocity, so 0.5pv^2 drops out of Bernoulli's law and we're left with 1.01*10^5 pascals (for the atmosphere) plus the hydrostatic pressure, i.e. pgh. Anyone agree with me?
 
Last edited:
Is anyone out there?
 
madchemist said:
But isn't there no such thing as NEGATIVE pressure?
A fluid cannot support tension, only compression. So you're right, the pressure cannot be negative.

I think that the person who devised this problem just made up the numbers without doing a reality check.
 
Thanks Doc Al and nasu! This problem is, in a sense, "solved".
 

Similar threads

Bernoulli equation / fluid flow / finding height
  • · Replies 6 ·
Replies
6
Views
3K
Bernoulli’s Equation and External Forces
  • · Replies 4 ·
Replies
4
Views
2K
Bernoulli Equation and gauge pressure
  • · Replies 5 ·
Replies
5
Views
4K
Force required to hold a fire hose
  • · Replies 13 ·
Replies
13
Views
20K
Bernoulli, Gauge pressure in hose?
  • · Replies 4 ·
Replies
4
Views
8K
Bernoulli's Principle Problem/Energy Conservation
  • · Replies 2 ·
Replies
2
Views
2K
Bernoulli Equation — Discharging water from a partially-filled sealed tank
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Exit velocity through a nozzle: Bernoulli vs. Experience
  • · Replies 7 ·
Replies
7
Views
4K
Fluid Dynamics: Calculating Speed and Force in Syringe Experiments"
  • · Replies 2 ·
Replies
2
Views
4K
Bernoulli's Equation and fire hose
  • · Replies 1 ·
Replies
1
Views
7K