How to Model the Volume of Water in a Graduated Cylinder with a Hole?

  • Thread starter Thread starter RagincajunLA
  • Start date Start date
  • Tags Tags
    Cylinder Volume
Click For Summary
SUMMARY

The discussion focuses on modeling the volume of water in a graduated cylinder with a hole at the bottom, specifically avoiding direct use of Torricelli's Law and Bernoulli's Principle. Key parameters include an initial volume of 1000 cm³, an outlet radius of 0.0018 m, a cylinder radius of 0.031 m, and an initial water height of 0.36 m. The participant is attempting to derive a differential equation using conservation of energy to calculate the water velocity and volume over time, but is struggling to match the expected data point of 950 cm³ at t=3.4s.

PREREQUISITES
  • Understanding of differential equations
  • Familiarity with fluid dynamics concepts
  • Knowledge of conservation of energy principles
  • Basic skills in mathematical modeling
NEXT STEPS
  • Research the derivation of Torricelli's Law and its application in fluid dynamics
  • Study the principles of conservation of energy in fluid systems
  • Explore numerical methods for solving differential equations
  • Investigate alternative modeling techniques for fluid flow without Bernoulli's Principle
USEFUL FOR

Students in physics or engineering, particularly those studying fluid dynamics and mathematical modeling of physical systems.

RagincajunLA
Messages
19
Reaction score
0
Hey guys, its my first time posting and i really need some help with a problem.
I have an experiment of a graduated cylinder with a hole at the bottom of it. I basically need to model a differential equation to give the volume of water in the cylinder at any given time. I am not allowed to directly use torriciellis law or bernoullis principal, but i can show the derivation of them for the answer.

A few key measurements that are needed are:
Initial Volume = 1000cm^3 = .001m^3
radius of outlet=.0018m
radius of cylinder = .031m
Initial height of water = .36m

All help would be appreciated, I am really stuck and have been at this for hours :/
 
Physics news on Phys.org
I can't think of anything not involving Bernoulli's. What have you been learning in class?
 
well the thing is, we can't explicitly use bernoullis/torricielli's but if we show the derivation, then that's ok. I was on the track of using conservation of energy to find the velocity of the water leaving the cylinder. but when i do everything out and find the equation for volume, I am very far off from the first data point which is t=3.4s and volume=950cm^3=9.5e-4
 

Similar threads

Sinking a cylinder with varying hole sizes
  • · Replies 97 ·
4
Replies
97
Views
15K
What is the relationship between pressure and flow rate?
  • · Replies 8 ·
Replies
8
Views
4K
Stability of a floating cylinder
  • · Replies 7 ·
Replies
7
Views
3K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
  • · Replies 40 ·
2
Replies
40
Views
6K
Water flowing from one vertical cylinder to another
  • · Replies 1 ·
Replies
1
Views
2K
Trouble solving for end state of two control volumes in a rigid tank
  • · Replies 12 ·
Replies
12
Views
3K
How Does Pressure Affect the Buoyancy of a Cylinder?
  • · Replies 2 ·
Replies
2
Views
2K
Depth of a basketball floating on water
  • · Replies 9 ·
Replies
9
Views
1K
Rate of Increase in Water Level Due to Falling Cone in Cylinder
  • · Replies 6 ·
Replies
6
Views
3K
E-field in a cylinder with a hole parallel to its axis
  • · Replies 1 ·
Replies
1
Views
3K