A spray tank system is engineered to uniformly distribute a pest-control liquid across plants by using a pressurized mechanism. The tank, pressurized to 150 kPa, holds the pesticide at a height of 0.80 meters. Liquid flows from the tank through a 1.9 meter pipe with a diameter of 0.015 meters, angled at 0.698 radians, ultimately reaching a 0.007 meter nozzle that sprays the pesticide. Accurate calculation of the system's flow rate is crucial to ensure uniform application, and this is achieved by first determining the flow velocity within the connecting pipe.

The design requires an understanding of fluid mechanics principles. At the outset, the velocity of the fluid in the tank at Point 1 is zero, with the pressure set to 150 kPa. Point 2, located at the nozzle, is assumed to be open to the atmosphere, with a pressure of zero. The height difference between Points 1 and 2, calculated using the 0.698-radian pipe angle and pipe length, determines the elevation change component in the Bernoulli equation. This height difference is found by multiplying the pipe length by the sine of the inclination angle.

To connect the parameters at Points 1 and 2, a modified Bernoulli equation is used, accounting for energy losses due to friction and the nozzle's loss coefficient. The equation expresses the pressure, velocity, and elevation terms for both points as follows:

Here, p represents pressure, ρ the fluid density, V the velocity, g the gravitational acceleration, z₁ the height of the pesticide inside the tank, and z₂ the nozzle height above the bottom of the tank. With values substituted for these terms, the flow velocity in the pipe at Point 1 is solved.

After calculating the pipe's flow velocity, the flow rate, Q, is determined by multiplying this velocity by the cross-sectional area A of the pipe:

Where A is:

This flow rate calculation ensures that the pesticide is delivered at a consistent and effective rate, optimizing pest control application.