How Does Atmospheric Pressure Affect Water Stream Shrinkage?

[dmk90]

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?

Homework Equations

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]

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

 

[dmk90]

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]

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.