Pascal's principle/pressure/viscosity

  • Thread starter ally1h
  • Start date
In summary, we are given a large storage tank filled with water with 2 pipes at the bottom. The large pipe has a diameter of 0.1m and the small pipe has a diameter of 0.05m and a length of 20m. Point A has an absolute pressure of 1.95x10^5 Pa and a velocity of 6 m/s. We are asked to determine the atmospheric pressure, the rate of water leaving the tank, the time it takes to empty the tank, the water velocity and pressure at point B, and the amount of force needed to keep a patch in place at point C."
  • #1
ally1h
61
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
  • #3


I can provide a response to this problem by breaking it down into smaller parts and using relevant principles and equations to solve it.

Firstly, Pascal's principle states that pressure applied to an enclosed fluid is transmitted equally in all directions. This means that the pressure at point A, where the water is flowing out of the large pipe, is equal to the pressure at point B, where the water is flowing into the smaller pipe. This also means that the pressure at point B is equal to the atmospheric pressure.

Using the given information, we can calculate the pressure at point B as follows:

P = ρgh + Patm

Where P is the pressure at point B, ρ is the density of water, g is the acceleration due to gravity, h is the height of the water above point B, and Patm is the atmospheric pressure.

Since the water is at the same height at points A, B, and C, we can set h = 0.5m. Substituting in the values given, we get:

P = (1000 kg/m^3)(9.8 m/s^2)(0.5m) + Patm
P = 4900 Pa + Patm

Next, we can solve for the atmospheric pressure by using the given pressure at point A:

1.95x10^5 Pa = 4900 Pa + Patm
Patm = 1.901x10^5 Pa

This is the answer to part a) of the problem.

For part b), we can use the equation Q = Av, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. Since the flow rate is the same at points A and B, we can set Q = Av for both pipes and equate them:

Av1 = Av2
(6 m/s)(π(0.05m)^2) = Q
Q = 4.71x10^-3 m^3/s

This is the amount of water that leaves the tank each second through the smaller pipe.

For part c), we can use the equation t = V/Q, where t is the time it takes to empty the tank, V is the volume of the tank, and Q is the flow rate. The volume of the tank can be calculated using the formula V = πr^2h, where r is the radius of the tank
 

1. What is Pascal's principle?

Pascal's principle, also known as the principle of transmission of fluid-pressure, states that a change in pressure applied to an enclosed fluid will be transmitted undiminished to every part of the fluid and to the walls of the container.

2. How does Pascal's principle relate to pressure?

Pascal's principle is the basis for understanding how pressure works in fluids. It explains how changes in pressure at one point in a fluid will cause a change in pressure throughout the entire fluid.

3. What is pressure?

Pressure is defined as the force applied per unit area. In the context of fluids, it is the amount of force exerted by the fluid on the walls of its container.

4. How does viscosity affect fluid pressure?

Viscosity is a measure of a fluid's resistance to flow. In general, more viscous fluids will have higher pressure because they require more force to flow through a given area compared to less viscous fluids.

5. How does Pascal's principle apply to hydraulic systems?

Pascal's principle is the basis for hydraulic systems, which use pressurized fluids to transmit force and energy. By applying a small force to a small area, a larger force can be generated at a larger area due to the undiminished transmission of pressure throughout the fluid.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
9K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
952
  • Introductory Physics Homework Help
Replies
6
Views
10K
  • Introductory Physics Homework Help
Replies
2
Views
11K
  • Introductory Physics Homework Help
Replies
15
Views
4K
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
18
Views
3K
Back
Top