Problem: Water flows from the pipe shown in the figure with a speed of 8.0 m/s. (Figure 1)What is the height h of the standing column of water? Express your answer to two significant figures and include the appropriate units.

Continuity equation:

$\boxed{\mathbf{Av}\mathbf{=}\mathit{c}\mathit{o}\mathit{n}\mathit{s}\mathbf{tan}\mathit{t}}$

Bernoulli’s equation:

$\boxed{{\mathbf{P}}_{\mathbf{1}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\rho }{{\mathbf{v}}_{\mathbf{1}}}^{\mathbf{2}}\mathbf{+}\mathbf{\rho }\mathbf{g}{\mathbf{y}}_{\mathbf{1}}\mathbf{=}{\mathbf{P}}_{\mathbf{2}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\rho }{{\mathbf{v}}_{\mathbf{2}}}^{\mathbf{2}}\mathbf{+}\mathbf{\rho }\mathbf{g}{\mathbf{y}}_{\mathbf{2}}}$

We'll use 1 to identify the inlet and 2 to identify the outlet.

A₁ = 10 cm² 

A₂ = 5 cm²

v₂ = 8.0 m/s

A₁v₁ = A₂v₂

v₁ = (A₂v₂)/A₁ = (5 ×  8.0)/10 = 4.0 m/s

Using the inlet as the reference point: