Question

For a steady-state, fully developed laminar flow of a Newtonian fluid through a cylindrical pipe at a constant volumetric flow rate, which of the following statements regarding the pressure drop across the pipe (\(\Delta P\)) is/are TRUE?

• A. \(\Delta P\) increases with fluid viscosity
• B. \(\Delta P\) increases with pipe length
• C. \(\Delta P\) increases with pipe diameter
• D. \(\Delta P\) remains unchanged with fluid viscosity

Hint:

In fluid dynamics, pressure drop in pipes depends on factors such as fluid viscosity, pipe length, and diameter. Keep these relationships in mind when analyzing flow systems.

Answer 1

The Correct Option is A, B

Step 1: Understand the Relationship Between Pressure Drop and Viscosity.
For laminar flow in a pipe, the pressure drop (\(\Delta P\)) is directly proportional to the fluid viscosity, which means higher viscosity increases the pressure drop. Hence, Option (A) is true. 
Step 2: Understand the Relationship Between Pressure Drop and Pipe Length.
The pressure drop increases with the length of the pipe. Longer pipes offer more resistance to flow, so Option (B) is also true. 
Step 3: Understand the Relationship Between Pressure Drop and Pipe Diameter.
The pressure drop decreases with an increase in pipe diameter because the resistance to flow decreases. 
Therefore, Option (C) is false. 
Step 4: Confirm the Inverse Relationship with Viscosity.
Since pressure drop depends on viscosity, Option (D) is false.