Help with Bernoulli's equation

In summary, a large water tank sits at the top of a hill with an open top. A pipe leads downhill from the bottom of the tank and gradually narrows in diameter from 5.0 cm at point A to 3.0 cm at point B, which is 12.0 m below the water surface in the tank. The velocity at point A is 4.0 m/s and the question asks to calculate the absolute pressure at point B. Using Bernoulli's equation and given values for pressure, density, and velocity at point A, we can calculate the pressure at point B. The given answer in the exam booklet has a value of 0 for v1, which is likely due to the assumption that the
  • #1
TheCurator
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0

Homework Statement



Q. A large water tank, open at the top, is situated at the top of a hill. A pipe leads downhill from
the bottom of the tank. The pipe has a diameter 5.0 cm where it is attached to the tank at point
A, but gradually narrows to a diameter of 3.0 cm at a point B which is 12.0 m below the
surface level of the water in the tank.
Velocity at A is 4.0 ms.

(ii) Calculate the absolute pressure at the lower level (point B).

Homework Equations



Values:
p1 = pO = 1.01 * 10^5
P(density) = 1.00 * 10^3
v1 = 4.0 (back to this in a second)
y1 = 0 (assume, since the question indicates nothing else)

p2 = ?
v2 = (v1A1)/A2 = 11 ms
y2 = 12 m

Rearrange bernoullis;

p2 = p1 + 1/2P(v1^2 - v2^2) + Pg(y1 - y2)
Sub in, calculate to get answer.

The answer given in the exam booklet gives v1 as 0, while y1 = 12 and y2 = 0.
I'm pretty sure the y values were swapped because it essentially achieves the same purpose, ie. the distance between the two points.
However, I have no idea as why v1 would be 0. Any help?
The booklet also states that we assume the tank to be large, so v1 ~ 0. Why can't we use the v1 = 4 value, however?
 
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  • #2
The book is comparing a point at the water surface (not at point A) to point B. You only have partial information about point A, so it's less useful. (What's the height of point A? The pressure?)
 
  • #3
Thanks!
 

Related to Help with Bernoulli's equation

1. What is Bernoulli's equation?

Bernoulli's equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation of a fluid at a single point in time. It states that the sum of the kinetic energy, potential energy, and internal energy of a fluid remains constant as it flows.

2. How is Bernoulli's equation derived?

Bernoulli's equation can be derived from the conservation of energy principle and the application of the Bernoulli's principle, which states that the pressure of a fluid decreases as its velocity increases. It can also be derived from the Euler equations in fluid dynamics.

3. What are the applications of Bernoulli's equation?

Bernoulli's equation has many practical applications, including calculating the lift force on an airplane wing, determining the flow rate of a fluid through a pipe, and understanding the principles of aerodynamics in designing vehicles such as cars and airplanes.

4. What are the limitations of Bernoulli's equation?

Bernoulli's equation assumes that the fluid is incompressible, inviscid, and steady, which is not always the case in real-world scenarios. It also does not take into account external forces, such as friction and turbulence, which can affect the behavior of the fluid.

5. How can Bernoulli's equation be applied to solve problems?

To solve problems using Bernoulli's equation, you need to identify the known and unknown variables, such as pressure, velocity, and elevation, and apply the equation to solve for the unknown variable. It is also important to carefully consider the assumptions and limitations of the equation to ensure accurate results.

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