Continuity for incompressible steady flow in a pipe True or False: For an incompressible liquid flowing continuously through a pipe, the discharge (quantity per second) is different at different sections.

Introduction:
The continuity equation is a cornerstone of fluid mechanics. For incompressible steady flow, it asserts constancy of volumetric flow rate along a streamline (and through any cross-section of a pipe), regardless of local changes in area and velocity.

Given Data / Assumptions:

• Incompressible liquid (density constant).
• Steady flow (no accumulation with time).
• No leakage or branching between the two sections being compared.

Concept / Approach:
Continuity for incompressible steady flow: A1 * V1 = A2 * V2 = Q (constant). If the pipe diameter changes, velocity adjusts inversely with area to keep Q the same. Therefore, the statement that discharge is “different at different sections” is false.

Step-by-Step Solution:

Verification / Alternative check:
Measurement devices placed at different diameters show different velocities but the same volumetric flow rate when the system is closed and steady, validating continuity.

Why Other Options Are Wrong:

• True: contradicts continuity.
• Depends only on viscosity: viscosity affects losses and profiles, not mass conservation.
• True only in laminar/turbulent: regime does not change mass conservation.

Common Pitfalls:
Confusing velocity changes with discharge changes. Remember that velocity can vary with area while Q remains constant.

Final Answer:
False