Continuity equation:

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

Bernoulli’s equation:

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

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

A_{1} = 10 cm^{2}

A_{2} = 5 cm^{2}

v_{2} = 8.0 m/s

A_{1}v_{1} = A_{2}v_{2}

v_{1} = (A_{2}v_{2})/A_{1} = (5 × 8.0)/10 = 4.0 m/s

Using the inlet as the reference point:

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.

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