Time taken for fluid to start flowing

[springwave]

Homework Statement

A large container has of diameter D has a small orifice or diameter d at it's bottom,
When the orifice is opened, liquid of density ρ starts flowing out with an approximate velocity of √2gh, but the liquid takes some time τ to reach this velocity. Find the approximate order of magnitude of τ.

What is the acceleration of the bottom layer of the liquid, at the instant when the orifice is opened.

Homework Equations

Pascals law
Bernoullis equation

The Attempt at a Solution

If we find the initial acceleration, then it will be quite easy to find the time.
And to do this, I did the following:

Taking a small mass element Δm near the bottom, covering a of length Δx, and using force = pressure * area; I found acceleration = gh/Δx

I don't know how to proceed om here.
It would be great if someone could explain to me, how to analyze the motion of the liquid during this small interval of time, from the instant of release to start of steady flow

 

[Spinnor]

Treat the column of water directly above the orifice as a freely accelerating object?

F = ρvg = ρva

 

[springwave]

We can't do that because, the walls of the container (bottom) exert upward force on the column

 

[Spinnor]

We can't do that because, the walls of the container (bottom) exert upward force on the column

I said the column directly above the orifice. It was just for an estimate.