(II)What gauge pressure in the water pipes is necessary if a fire hose is to spray water to a height of 16 m?

Bernoulli’s equation reduced form for obtaining pressure variation with height states that change in pressure of the fluid is a product of density, earth’s gravitational acceleration, and height difference.

The height is \(\Delta h = 16\;{\rm{m}}\).

The standard values for the density of water is \(\rho = 1000\;{\rm{kg/}}{{\rm{m}}^3}\), and the gravitational acceleration is \(g = 9.81\;{\rm{m/}}{{\rm{s}}^2}\).

The gauge pressure needed by the water pipes is calculated below:

\(P = \rho g\Delta h\)

Substituting the values in the above equation.

\(\begin{array}{c}P = \left( {1000\;{\rm{kg/}}{{\rm{m}}^3}} \right)\left( {9.81\;{\rm{m/}}{{\rm{s}}^2}} \right)\left( {16\;{\rm{m}}} \right)\\P = 156960\;{\rm{kg/m}} \cdot {{\rm{s}}^2}\end{array}\)

Hence, the gauge pressure needed by the water pipes is \(156960\;{\rm{kg/m}} \cdot {{\rm{s}}^2}\).