A pressure of approximately 1,025 Pa (or 1.02 kPa) must be maintained just upstream of the nozzle to deliver a flow rate of 0.0157 m³/s, calculated using the continuity equation and considering the change in cross-sectional area between the hose and the nozzle.
To determine the required pressure just upstream of the nozzle for a specified flow rate, the continuity equation, which states that the product of cross-sectional area and fluid velocity remains constant in a flowing system, is applied. Given the diameters of the hose and nozzle, the cross-sectional areas can be calculated. As the flow rate is constant throughout the system, the velocity of the fluid at the nozzle must increase due to the smaller cross-sectional area
The Bernoulli's equation is then utilized, taking into account the kinetic energy, potential energy, and pressure energy of the fluid. Neglecting changes in height and velocity, the equation simplifies to express the pressure drop between the hose and the nozzle. Solving for pressure, the result is approximately 1,025 Pa (or 1.02 kPa). Therefore, to meet the fire code requirement of a flow rate of 0.0157 m³/s through the nozzle, a pressure of around 1.02 kPa must be maintained just upstream of the nozzle.