**Pressure Drop in Laminar Flow of a Liquid in a Smooth Pipe**

**Introduction**
When a liquid flows through a smooth pipe, it can exhibit two types of flow regimes: laminar flow and turbulent flow. Laminar flow occurs at low velocities or high viscosities, where the fluid particles move in smooth layers parallel to the pipe walls. On the other hand, turbulent flow occurs at high velocities or low viscosities, where the fluid particles mix and swirl chaotically.

**Pressure Drop in Laminar Flow**
In laminar flow, the pressure drop is determined by the viscosity of the liquid, the flow rate, the length of the pipe, and the diameter of the pipe. However, the pressure drop is independent of the density of the liquid. This can be explained by considering the fundamental equations governing fluid flow.

**Hagen-Poiseuille Equation**
The Hagen-Poiseuille equation describes the pressure drop in laminar flow through a cylindrical pipe. The equation is given by:

ΔP = (8μLQ) / (πr^4)

where ΔP is the pressure drop, μ is the dynamic viscosity of the liquid, L is the length of the pipe, Q is the volumetric flow rate, and r is the radius of the pipe.

**Density's Effect on Laminar Flow**
If we analyze the Hagen-Poiseuille equation, we can see that the pressure drop is directly proportional to the dynamic viscosity, length of the pipe, and volumetric flow rate. However, the equation does not contain any term directly related to the density of the liquid.

This means that the pressure drop in laminar flow is independent of the density of the liquid. The density only affects the mass flow rate, which is the product of the volumetric flow rate and the density of the liquid. The pressure drop in laminar flow does not depend on the mass flow rate, only on the volumetric flow rate.

**Conclusion**
In conclusion, the pressure drop for laminar flow of a liquid in a smooth pipe is independent of the density of the liquid. The pressure drop is determined by the dynamic viscosity, length of the pipe, and volumetric flow rate. The Hagen-Poiseuille equation, which describes laminar flow, does not contain any term directly related to density.