Question

36. Flow rate for a particular nozzle is

• A. Directly proportional to pressure
• B. Inversely proportional to pressure
• C. Directly proportional to square root of the pressure
• D. Directly proportional to square of the pressure

Hint:

To double the flow rate of a nozzle, you must increase the pressure by four times (\(2^2 = 4\)).
Be careful: raising pressure too high to increase flow rate produces extremely fine droplets, which increases the risk of spray drift.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A spray nozzle functions as a small physical orifice through which pressurized liquid is discharged into the atmosphere.
The relationship between fluid flow rate and operating pressure is governed by the principles of fluid dynamics, specifically the orifice discharge equations.
Key Formula or Approach:
The discharge rate (\(Q\)) of liquid through an orifice is expressed using Torricelli's theorem and the orifice discharge equation:
\[ Q = C_d \cdot A \cdot \sqrt{\frac{2 \cdot P}{\rho}} \]
where \(C_d\) is the coefficient of discharge, \(A\) is the cross-sectional area of the nozzle orifice, \(P\) is the operating pressure, and \(\rho\) is the density of the spray liquid.
From this, we can establish the proportionality relation:
\[ Q \propto \sqrt{P} \]

Step 2: Detailed Explanation:
The velocity of liquid passing through a nozzle orifice is directly proportional to the square root of the applied pressure (\(v = \sqrt{2P/\rho}\)).
Since the volumetric flow rate (\(Q\)) is the product of the orifice area and the fluid velocity, the flow rate must also vary with the square root of the pressure:
\[ Q = K \cdot \sqrt{P} \]
where \(K\) is a constant representing the physical properties of the nozzle and fluid.
This mathematical relationship implies that to double the nozzle output flow rate (\(Q_2 = 2 Q_1\)), the operating pressure must be quadrupled (\(P_2 = 4 P_1\)):
\[ \frac{Q_2}{Q_1} = \sqrt{\frac{P_2}{P_1}} \]
Therefore, the flow rate is directly proportional to the square root of the pressure.

Step 3: Final Answer:
The flow rate for a particular nozzle is directly proportional to the square root of the pressure.