Pascal's principle/pressure/viscosity

  • Thread starter Thread starter ally1h
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on applying Pascal's principle to a fluid dynamics problem involving a large storage tank filled with water. Key parameters include a tank diameter of 10m, water density of 1000 kg/m³, and viscosity of 1.0x10^-3 Pa·s. The problem requires calculating atmospheric pressure, flow rate from a smaller pipe with a diameter of 0.05m, and the force needed to hold a patch over a square hole in the tank. The calculations utilize fundamental equations such as P = F/A and P = Patm + ρgd.

PREREQUISITES
  • Understanding of Pascal's principle in fluid mechanics
  • Knowledge of fluid properties: density and viscosity
  • Familiarity with pressure calculations in static fluids
  • Basic proficiency in algebra and unit conversions
NEXT STEPS
  • Calculate atmospheric pressure using P = Patm + ρgd
  • Determine flow rate from the smaller pipe using the continuity equation
  • Analyze the time required to empty the tank based on flow rate
  • Calculate the force exerted by the patch using P = F/A for the square hole
USEFUL FOR

Students in physics or engineering disciplines, particularly those studying fluid dynamics, as well as educators seeking to illustrate practical applications of Pascal's principle and fluid mechanics concepts.

ally1h
Messages
61
Reaction score
0

Homework Statement


A large storage tank (diameter 10m) is filled 10m deep with water (density= 1000 kg/m^3, viscosity= 1.0x10^-3 Pa*s). The outlet at the bottom consists of 2 pipes, as shown. The large pipe has a diameter d2= 0.1m, and the smaller have a diameter d3= 0.05m and length of 20m. A pressure and flow gauge at point A indicates an absolute pressure of 1.95x10^5 Pa, and a velocity of 6 m/s for the water inside the large pipe. You may assume points A,B, and C are all at the same height, and that the height is 0.5m above the bottom of the tank.

Link below takes you to the diagram...
http://farm4.static.flickr.com/3073/2728597416_16e9339014.jpg?v=0

a) Determine the atmospheric pressure. (Warning: it will not turn out to be exactly 1 atm.)

b) If the outlet of the small pipe is atmospheric pressure, how many cubic meters of water leave the tank each second?

c) How long will it take to empty the tank? (Assume the outward flw is a constant for this calculation!)

d) Find the water velocity and pressure at point B, inside the smaller pipe.

e) At point C, the storage tank has a square hole, 5cm x 5cm. A little dutch boy is holding a patch in place over the hole. How much force does he have to exert (horizontally) to keep the patch in place? Explain the reasoning.



Homework Equations


Pascal's Principle
101.3 Pa= 1 atm
P = F/A
P = Patm + ρgd



The Attempt at a Solution


Wow... I am baffled as to how I should even start this. Trying to a) brought me to exactly 1 atm so obviously THAT isn't correct. I am at a complete loss...

Please, someone help?
 
Physics news on Phys.org

Similar threads

How Does Bernoulli's Principle Apply to Fluid Flow in Pipes?
  • · Replies 1 ·
Replies
1
Views
3K
Viscosity finding the velocity at a point
  • · Replies 1 ·
Replies
1
Views
2K
Bernoulli's Equation and A Water Tank w/ Small Outlet
  • · Replies 2 ·
Replies
2
Views
12K
Finding speed of water leaving a pressurized vessel
  • · Replies 1 ·
Replies
1
Views
10K
Water flows from a compressed tank
  • · Replies 2 ·
Replies
2
Views
2K
Water Pressure in Pipe: 85L/s at 35m Depth
  • · Replies 18 ·
Replies
18
Views
4K
Understanding Pressure Drop Calculations in Fluid Mechanics
  • · Replies 6 ·
Replies
6
Views
12K
How Does Bernoulli's Principle Apply to Varying Pipe Diameters and Water Flow?
  • · Replies 3 ·
Replies
3
Views
2K
Problem about Hagen-Poiseuille law and pump
  • · Replies 15 ·
Replies
15
Views
5K
Pascal's Principle Homework: Pressure Variation w/ Height & Diameter
  • · Replies 4 ·
Replies
4
Views
2K