Engineers are designing a horizontal irrigation pipeline that carries fresh water…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
Engineers are designing a horizontal irrigation pipeline that carries fresh water from a reservoir to a row of sprinkler nozzles. At a particular section, the pipe has an internal area of 9.0×10−4m2 and carries water at 2.0ms−1. To improve coverage, the engineers will attach a nozzle of smaller, unknown internal radius to the end of this section.
Design requirements:
1. The nozzle must increase the water speed to 12ms−1.
2. The nozzle must sustain the same mass flow rate that currently passes through the pipe.
The water density can be taken as 1.0×103kgm−3, and elevation changes are negligible.
(a) Derive an expression for the required cross-sectional area of the nozzle in terms of quantities defined in the prompt.
(b) Calculate the numerical value of the nozzle’s internal radius that meets the design requirement.
(c) Determine the difference in static pressure between the pipeline section and the nozzle exit that must exist while the system operates as described. State clearly which location is at the higher pressure.
(d) If the design instead called for the water speed at the nozzle exit to double (rather than triple) relative to the pipe speed, explain quantitatively how the required nozzle radius and pressure difference would compare to those found in parts (b) and (c).