Why Is v1 Assumed to Be Zero in Bernoulli's Equation for a Large Tank?

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SUMMARY

The discussion centers on the application of Bernoulli's Equation in a scenario involving a large water tank and a pipe leading downhill. The key point is that the velocity at the water surface (v1) is assumed to be zero due to the large size of the tank, which allows for the simplification of calculations. The pressure at point B is derived using the formula p2 = p1 + 1/2P(v1^2 - v2^2) + Pg(y1 - y2), with specific values provided for pressure and density. The assumption of v1 being zero is justified as it represents the velocity at the water surface, which is negligible compared to the velocity at point B.

PREREQUISITES
  • Understanding of Bernoulli's Equation
  • Knowledge of fluid dynamics principles
  • Familiarity with pressure and velocity calculations in fluid systems
  • Basic algebra for rearranging equations
NEXT STEPS
  • Study the derivation and applications of Bernoulli's Equation in fluid mechanics
  • Learn about the assumptions made in fluid dynamics, particularly regarding large tanks
  • Explore the concept of velocity profiles in pipes with varying diameters
  • Investigate the impact of gravitational potential energy in fluid flow calculations
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Students studying fluid mechanics, engineers working with hydraulic systems, and anyone interested in understanding the principles of fluid dynamics and Bernoulli's Equation.

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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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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?)
 
Thanks!
 

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