Oil is flowing through a pipe of diameter 160 mm. If the density and viscosity of the oil are 9

step 1 We're given a diameter of 0 .16 meters, a density of 920, mu is 0 .390, and Q is 0 .06. The area

Oil is flowing through a pipe of diameter 160 mm. If the...

Oil is flowing through a pipe of diameter $160 \mathrm{~mm}$. If the density and viscosity of the oil are $920 \mathrm{~kg} / \mathrm{m}^{3}$ and 0.390 $\mathrm{N} \cdot \mathrm{s} / \mathrm{m}^{2}$, respectively, determine the drop in pressure caused by viscous friction over the $10-\mathrm{m}$ -long section for a flow of $0.06 \mathrm{~m}^{3} / \mathrm{s}$.

Key Concepts

Viscosity

A physical property of fluids that measures their resistance to shear or flow. Viscosity directly influences the magnitude of frictional forces within the fluid, affecting both the Reynolds number and the overall pressure drop due to friction in piping systems.

Continuity Equation

An expression of mass conservation that, in the context of pipe flow, relates the volumetric flow rate to the fluid velocity and the cross-sectional area of the pipe. It provides the necessary link to determine the average velocity from a given flow rate, which is then used in further calculations like those in the Darcy-Weisbach equation.

Friction Factor

A dimensionless coefficient that characterizes the resistance to flow due to friction along the pipe walls. The friction factor depends on the flow regime (as indicated by the Reynolds number) and the pipe’s roughness, and it is a key component in the Darcy-Weisbach equation for estimating pressure losses.

Reynolds Number

A dimensionless parameter that quantifies the ratio of inertial forces to viscous forces in a fluid flow. It is critical in determining the flow regime — laminar or turbulent — which in turn affects the choice of model or correlations (such as for friction factor) used in calculating pressure drops.

Darcy-Weisbach Equation

This is a fundamental relation in fluid mechanics used to calculate the pressure drop or head loss due to friction in pipe flow. It relates the frictional loss to factors such as the fluid velocity, pipe length, diameter, and friction factor, making it essential for analyzing how viscous effects dissipate energy in flowing fluids.

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