Short Answer:

The flow rate in a pipe increases significantly with an increase in pipe diameter. According to fluid mechanics principles, flow rate is directly related to the cross-sectional area of the pipe, which depends on the square of the diameter. Therefore, even a small increase in diameter results in a large increase in flow rate.

If other factors like pressure and pipe roughness remain the same, a larger diameter allows more fluid to pass through with less resistance and lower velocity loss. This principle is essential in the design of water supply and drainage systems in civil engineering.

Detailed Explanation:

Flow rate variation with pipe diameter

In fluid mechanics, understanding how the flow rate changes with pipe diameter is crucial for designing efficient piping systems. Flow rate refers to the volume of fluid passing through a pipe per unit time. It is commonly expressed in cubic meters per second (m³/s) or liters per second (L/s).

The flow rate (Q) is related to pipe diameter (D) primarily through two important equations:

1. Q = A × V
   Where:
   • QQQ = Flow rate
   • AAA = Cross-sectional area of the pipe = πD2/4\pi D^2 / 4πD2/4
   • VVV = Average velocity of fluid

This formula shows that flow rate increases with the square of the pipe diameter, because area A∝D2A \propto D^2A∝D2.

1. Darcy-Weisbach or Hazen-Williams equation
   These are used to estimate head loss or pressure drop and further show how larger diameter reduces friction loss, enabling more flow.

Effect of Diameter Increase

1. Doubling the Diameter
   If the diameter is doubled, the area increases by a factor of four (since A∝D2A \propto D^2A∝D2), so for a given velocity, the flow rate increases fourfold.
2. Friction and Head Loss
   In real-world systems, flow is also affected by pipe roughness and frictional head loss. A larger diameter results in lower velocity for the same flow, which reduces friction loss and allows the system to operate more efficiently.
3. Turbulent vs Laminar Flow
   In turbulent flow (common in large systems), the impact of diameter is even more significant. The flow rate depends on D2.63D^{2.63}D2.63 or higher (in Hazen-Williams formula), meaning a small increase in diameter causes a much larger increase in flow.

Engineering Applications

• Water Supply Systems
  Civil engineers use larger diameter pipes in main lines to handle high flow rates with minimum pressure drop.
• Sewerage and Drainage
  Sufficient diameter is chosen to ensure proper flow without clogging or overflow during peak usage.
• Fire Protection Systems
  High flow rate requirements make larger diameters essential to deliver enough water quickly.
• Irrigation Networks
  Accurate diameter sizing ensures balanced distribution of water to all fields with minimal energy loss.
• Industrial Fluid Transport
  In factories and plants, precise diameter calculations are used to handle specific chemical or water flows under different pressures.

Summary of Flow Rate vs. Diameter Relationship

• Flow rate is directly proportional to the square of the diameter when velocity is constant.
• In pressurized systems, increasing diameter also reduces velocity, which reduces frictional losses.
• Higher diameter allows higher flow with lower pressure requirement.
• Cost and space limitations must also be considered when increasing diameter.

Conclusion:

Flow rate increases sharply with pipe diameter due to the squared relationship with cross-sectional area. In practical systems, a larger diameter also reduces friction losses, enabling more efficient flow. This principle is key in civil engineering to optimize water supply, drainage, and other pipeline systems for performance and cost.