Finding pressure at narrow end of segment

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In summary: To simplify things, I simplified the equation to just use ρ. The pressure at the smaller end of the segment is 1.20 x 10^5 Pa.
  • #1
sona1177
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Homework Statement


A horizontal segment of pipe tapers from a cross-sectional area of 50.0 cm^2. The pressure at the larger end of the pipe is 1.20 x 10^5 Pa and the speed is .040 m/s. What is the pressure at the narrow end of the segment?


Homework Equations


I know how to do the problem using Bernoulli's equation but why can't I manage to get the correct answer using P=rho(g)(d). where rho=1000, g=9.8, and d=.00798 m


The Attempt at a Solution


 
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  • #2
Could you explain what d is in your equation.
As the pipe is horizontal there is no potential energy consideration.
I also note that there is no information given about the change in the cross section area.
Maybe you could clarify the question?
 
  • #3
Stonebridge said:
Could you explain what d is in your equation.
As the pipe is horizontal there is no potential energy consideration.
I also note that there is no information given about the change in the cross section area.
Maybe you could clarify the question?

d is the length of the narrow segment which I obtained by dividing area/pi and taking the sq root to get the radius. I then multiplied that by 2.
 
  • #4
Stonebridge said:
Could you explain what d is in your equation.
As the pipe is horizontal there is no potential energy consideration.
I also note that there is no information given about the change in the cross section area.
Maybe you could clarify the question?

Ooops! Sorry about leaving that info out. It tapers from 50-> 5 cm^2
 
  • #5
I don't quite understand what you are doing here.
The expression ρhg in the Bernoulli formula includes the terms
ρ the density of the fluid
g acceleration due to gravity
h the height of the liquid above the reference level
You have written ρdg but stated that d is "the length of the narrow segment". However, your calculation looks like it is for the diameter of the narrow segment.
Neither of these values, length or diameter, are the ones in the expression.
As the tube is horizontal, you don't need this term anyway, you just need the terms
½ρv² and p to find the pressure.
The value of v is found from the volume flowing per second being equal in both parts of the tube.
 

1. What is the relationship between pressure and the narrow end of a segment?

The pressure at the narrow end of a segment is inversely proportional to the cross-sectional area of the segment. This means that as the cross-sectional area decreases, the pressure at the narrow end increases.

2. How can I find the pressure at the narrow end of a segment?

To find the pressure at the narrow end of a segment, you can use the equation P = F/A, where P is pressure, F is the force applied to the segment, and A is the cross-sectional area of the segment. You will need to know the force and the cross-sectional area to calculate the pressure.

3. What factors can affect the pressure at the narrow end of a segment?

The pressure at the narrow end of a segment can be affected by several factors including the force applied, the cross-sectional area, the material of the segment, and the velocity of the fluid or gas passing through the segment.

4. How does the pressure at the narrow end of a segment affect the flow of fluid or gas?

The pressure at the narrow end of a segment can affect the flow of fluid or gas by creating a pressure gradient, which causes the fluid or gas to move from an area of high pressure to an area of low pressure. This can result in increased flow rate or turbulence depending on the specific conditions.

5. Can the pressure at the narrow end of a segment be controlled or changed?

Yes, the pressure at the narrow end of a segment can be controlled or changed by adjusting the factors that affect it, such as the force, cross-sectional area, or velocity. Additionally, devices such as valves or pumps can be used to manipulate the pressure at the narrow end of a segment.

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