Question

Flow rate of a particular nozzle used for spraying liquid pesticides is proportional to

• A. Pressure of spray material
• B. Volume of spray material
• C. Square of volume of spray material
• D. Square root of pressure of spray material

Hint:

To double the flow rate ($2\times$), you must increase pressure by $4\times$ ($2^2 = 4$) because $Q \propto \sqrt{P}$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Hydraulic sprayer nozzles discharge liquid through a calibrated orifice governed by Torricelli's and Bernoulli's orifice flow discharge equations.
Key Formula or Approach:
\[ Q = C_d \cdot A \cdot \sqrt{\frac{2\Delta P}{\rho}} \implies Q \propto \sqrt{P} \]
or \[ \frac{Q_1}{Q_2} = \sqrt{\frac{P_1}{P_2}} \]

Step 2: Detailed Explanation:
From the orifice flow equation, discharge \(Q\) through a spray nozzle varies directly with the orifice area \(A\) and the square root of the operating hydraulic pressure \(P\).
Therefore, to double the nozzle flow rate, the spray operating pressure must be quadrupled (increased 4-fold).

Step 3: Final Answer:
Thus, flow rate is proportional to the square root of pressure of spray material, matching option (D).