Calculate the viscosity of a fluid that would allow a...

Calculate the viscosity of a fluid that would allow a pressure drop of $35 \mathrm{kPa}$ over a 5 -m length of $3 / 4$-in. stainless steel sanitary pipe if the fluid is flowing at $2 \mathrm{~L} / \mathrm{min}$ and has a density of 1010 $\mathrm{kg} / \mathrm{m}^3$. Assume laminar flow.

Key Concepts

Volumetric Flow Rate

Volumetric flow rate is the volume of fluid passing through a given cross-sectional area per unit time. It connects directly to the fluid velocity and pipe geometry and is essential in calculations involving pressure drop and viscosity in fluid systems.

Hagen-Poiseuille Equation

This equation relates the pressure drop, flow rate, viscosity, and dimensions of a circular pipe for a Newtonian fluid under laminar flow conditions. It provides the theoretical basis for calculating one variable if the others are known and is fundamental when dealing with viscous flow in pipes.

Laminar Flow

Laminar flow is a flow regime characterized by smooth, orderly fluid motion in parallel layers with little to no mixing or turbulence between them. It is important in fluid mechanics because many analytical solutions, including the Hagen-Poiseuille equation, assume laminar conditions to simplify the relationship between variables such as pressure drop, flow rate, and viscosity.

Dynamic Viscosity

Dynamic viscosity is a measure of a fluid's resistance to flow and deformation. It quantifies the internal friction within the fluid as its molecules interact, making it a critical property in determining how much force is required to move the fluid through confined spaces like pipes.

Pressure Drop

Pressure drop refers to the loss of pressure in a fluid as it flows through a pipe, caused primarily by frictional forces between the fluid layers and the pipe wall. It is a key parameter in pipe flow analysis as it directly influences the flow rate and the energy required to maintain flow.

Pipe Geometry

Pipe geometry, including the internal diameter and length of the pipe, plays a crucial role in fluid flow calculations. Accurate knowledge of these dimensions ensures correct application of formulas like the Hagen-Poiseuille equation, as they directly affect the resistance to flow and the resulting pressure drop.

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