Step $5$: Bernoulli Pressure Drop Calculation Activity

Make a new sheet and call it "Bernoulli Aqueducts".

The final objective will be to make a bar graph.

Instructions:

Problem Setup:

$-$We have a table that shows the Bernoulli values for some Roman aqueducts.

Enter values for the missing cells for any row that does not have a corresponding pressure drop. These values should be initial velocity, final velocity, initial height, or final height.

For aqueducts where the pressure drop is known, you will solve for the other value using your knowledge of the Bernoulli equation.

Bernoulli Equation

$\frac{P_1}{g}+\frac{v_1^2}{2g}+z_1=\frac{P_2}{g}+\frac{v_2^2}{2g}+z_2$

Bernoulli Table for Aqueducts

$\backslash$table$[[$Aqueduct$,\backslash$table$[[$Initial Velocity$],[$v$\_(1)($m$/$s$)]],\backslash$table$[[$Final Velocity v$\_(2)],[($m$/$s$)]],\backslash$table$[[$Initial Height z$\_(1)],[($m$)]],\backslash$table$[[$Final Height z$\_(2)],[($m$)]],\backslash$table$[[$Pressure Drop$],[\backslash$Delta P$($Pa$)]]],[$Florence$,0\mathrm{.}5,5,50,10,],[$Venice$,1,4\mathrm{.}5,,15,383,895],[$Rome$,0\mathrm{.}8,6,,20,],[$Milan$,0\mathrm{.}6,7,60,25,],[$Naples$,1\mathrm{.}2,,55,12,],[$Genoa$,,6\mathrm{.}2,35,8,],[$Pisa$,0\mathrm{.}7,,70,20,],[$Siena$,1\mathrm{.}5,4\mathrm{.}2,,18,],[$Bologna$,0\mathrm{.}4,6\mathrm{.}8,80,,661,060],[$Verona$,,5\mathrm{.}3,65,28,535,355]]$