Question

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

Short answer

The necessary gauge pressure in the water pipes is \(156960\;{\rm{kg/m}} \cdot {{\rm{s}}^2}\).

Step-by-step solution

Understanding Bernoulli’s equation

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.

Given data

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 \(g = 9.81\;{\rm{m/}}{{\rm{s}}^2}\).

Evaluating the gauge pressure needed by the water pipes by using Bernoulli’s equation reduced form for obtaining pressure variation with height

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 \(156960\;{\rm{kg/m}} \cdot {{\rm{s}}^2}\).