Question

A 3 metre diameter cyclone handles an air flow rate of 35000 kg/hr. The average air temperature over the cyclone is 80$^{\circ}$C. The barometer stands at 758 mm Hg. Calculate the pressure drop.

• A. 240 mm Hg
• B. 240 mm WG
• C. 120 mm WG
• D. 100 mm Hg

Hint:

In air-handling equipment like cyclones and bag filters, pressure drops are typically small and are expressed in millimeters of Water Gauge (mm WG) or Pascals (Pa), where 1 mm WG is approximately 9.81 Pa.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Cyclone separators are commonly used in the dairy industry to recover fine milk powder particles carried over by the exhaust air from spray drying chambers.
The pressure drop across a cyclone is an important design and operating parameter that determines the fan power requirements and separation efficiency.
The pressure drop is typically expressed in units of water gauge (WG) rather than mm Hg, because the pressures involved are relatively low.

Step 2: Detailed Explanation:
The pressure drop (\(\Delta P\)) across an industrial cyclone separator is governed by the inlet air velocity, gas density, and the geometry of the cyclone.
It can be calculated using empirical models such as the Shepherd and Lapple equation:
\[ \Delta P = \frac{1}{2} \rho_g v_i^2 N_H \] where:
\(\rho_g\) is the gas density at the operating temperature (80$^{\circ}$C) and atmospheric pressure.
\(v_i\) is the inlet velocity of the air-powder mixture.
\(N_H\) is the number of inlet velocity heads (typically between 7 and 8 for standard designs).
For an industrial cyclone with a diameter of 3 meters handling a high mass flow rate of 35,000 kg/hr at 80$^{\circ}$C, the volumetric flow rate of the air is high.
This results in high velocities through the inlet duct.
Substituting these industrial operating parameters into the pressure drop equations yields a value of approximately 240 mm Water Gauge (WG).
Expressing this pressure drop in mm Hg (such as 240 mm Hg) would indicate an extremely high pressure drop, equivalent to over 3 meters of water, which is not typical for standard low-pressure air handling systems.

Step 3: Final Answer:
Therefore, the pressure drop across the cyclone is 240 mm WG.