How to find the difference in hieght in a u-tube(Please help)

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SUMMARY

The discussion focuses on calculating the difference in height in a U-shaped tube based on fluid dynamics principles. The problem involves a horizontal pipe with a cross-sectional area of 40.0 cm² at the wider section and 10.0 cm² at the constriction, with a water discharge rate of 6.00 x 10⁻³ m³/s. The calculated flow speeds are 1.5 m/s at the wide section and 6.0 m/s at the constricted area, leading to a pressure difference of 16,875 Pa. The height difference in the mercury columns was initially calculated as 0.127 m, which was later questioned for accuracy.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Knowledge of the continuity equation (AV = volume flow rate).
  • Familiarity with the properties of fluids, including density (e.g., density of mercury ρHg = 13.6 x 10³ kg/m³ and water ρw = 1.0 x 10³ kg/m³).
  • Ability to perform calculations involving pressure differences and height in fluid columns.
NEXT STEPS
  • Study Bernoulli's equation in detail to understand its application in fluid flow scenarios.
  • Learn about the continuity equation and its implications for flow rates in varying cross-sectional areas.
  • Explore the concept of hydrostatic pressure and its role in determining height differences in fluid columns.
  • Review examples of U-tube manometer calculations to reinforce understanding of pressure measurement in fluids.
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Students studying fluid mechanics, engineers working with fluid systems, and anyone interested in practical applications of fluid dynamics in real-world scenarios.

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Homework Statement


Help! How to find the difference in height in a u shaped tube?
1. Homework Statement

The horizontal pipe, shown in the figure, has a cross-sectional area of 40,0cm2 at the wider portions and 10,0cm2 at the constriction. Water is flowing in the pipe, and the discharge from the pipe is 6,00∗10−3m3s(6,00Ls). The density of mercury is ρHg=13,6∗103kgm3 and the density of water is ρw=1,00∗103kgm3.
Find
a)the flow speeds at the wide and the narrow portions
b)the pressure difference between these portions
c) the difference in height between the mercury columns in the U-shaped tube?

hint(Express the pressure at the lower mercury-water interface in two ways and uzse these expressions to solve for h)

1 minute ago
- 4 days left to answer.

Additional Details
This is the image of the situation:
http://session.masteringphysics.com/problemAsset/1260675/1/YF-14-45.jpg
please can someone help

Homework Equations


for a) i use AV=volume flow rate
b)used Bernoullis eqn and made the heights 0
c) used p=p1 and p=p2+density*g*h

The Attempt at a Solution


a) got v at large area=6m/s
v at constricted area=1.5m/s
b)got difference in presure to be 16875pa
c)got 0.127m which is apparently wrong
 
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Shouldn't the velocity in the constricted area be higher than the rest of the pipe?
 
Sorry i typed it in wrong they are the other way round
velocity at the constricted is 6m/s
velocity at the large is 1,5m/s
 
Did you use Bernoulli's equation of flow to get the pressure difference?
 
1. Homework Statement [/b]
Help! How to find the difference in height in a u shaped tube?
1. Homework Statement

The horizontal pipe, shown in the figure, has a cross-sectional area of 40,0cm2 at the wider portions and 10,0cm2 at the constriction. Water is flowing in the pipe, and the discharge from the pipe is 6,00∗10−3m3s(6,00Ls). The density of mercury is ρHg=13,6∗103kgm3 and the density of water is ρw=1,00∗103kgm3.
Find
a)the flow speeds at the wide and the narrow portions
b)the pressure difference between these portions
c) the difference in height between the mercury columns in the U-shaped tube?

hint(Express the pressure at the lower mercury-water interface in two ways and uzse these expressions to solve for h)

1 minute ago
- 4 days left to answer.

Additional Details
This is the image of the situation:
http://session.masteringphysics.com/problemAsset/1260675/1/YF-14-45.jpg
please can someone help

Homework Equations


for a) i use AV=volume flow rate
b)used Bernoullis eqn and made the heights 0
c) used p=p1 and p=p2+density*g*h

The Attempt at a Solution


a) got v at large area=1.5m/s
v at constricted area=6m/s
b)got difference in presure to be 16875pa
c)got 0.127m which is apparently wrong
 
Yes i did you and made the heights 0 because they on the same level.
 
I can't see what is wrong with your calculations. They seem legitimate. What are the expected answers for pressure and velocities in your source?
 
I don't know that's the problem. I thought it was wrong because someone said that they got this answer and apparently it was wrong but now that you confirmed what I thought maybe he was wrong. Thanks
 

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