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

AI Thread Summary
In the discussion about Bernoulli's equation for a large water tank, it is clarified that v1 is assumed to be zero because the tank's surface area is significantly larger than the pipe's diameter, leading to negligible velocity at the surface. The problem involves calculating the absolute pressure at point B, which is 12 meters below the water surface, using the given velocities and pressures. The confusion arises from the exam booklet stating v1 as zero while the velocity at point A is given as 4.0 m/s. The key point is that the comparison is made between the water surface and point B, where the velocity at the surface is effectively zero due to the tank's large size. This assumption simplifies the calculations and aligns with the principles of fluid dynamics.
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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?)
 
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