Water pressure problem

Homework Statement

Water flows through a hole at the bottom of a tank that is filled to a height h=3m. The radius of the hole is r1 = 1.5 cm.
1. What is the speed of the water immediately after it leaves the hole?

2. At what distance d below the bottom of the tank is the radius of the stream reduced to r2 = 1 cm?

The Attempt at a Solution

I managed to solve the speed for 7.7 m/s. However, I'm not sure what formula to use to address the atmospheric pressure that cause the stream to shrink.

Chestermiller
Mentor
The stream shrinks because it is accelerating gravitationally. As it speeds up, for the flow rate to remain constant, the cross sectional area must decrease.

Chet

Based on your clarification, I calculated the velocity at the bottom using the conservation of volumetric flow rate (R = Av = constant), v0 = 17.3. Then g = dv/dt -> dt = dv/g = 0.98 s. Then d = d0 + v0t + 0.5at2 = 12.3, which seems to be the correct result. What do you think?

Chestermiller
Mentor
Based on your clarification, I calculated the velocity at the bottom using the conservation of volumetric flow rate (R = Av = constant), v0 = 17.3. Then g = dv/dt -> dt = dv/g = 0.98 s. Then d = d0 + v0t + 0.5at2 = 12.3, which seems to be the correct result. What do you think?
I haven't checked your arithmetic, but you seem to have the right idea.