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

step 1 We're using the same pipe from the previous question, NQ is 0 .005 cubic meters per second. The

The 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 -m-long section for a flow of $0.005 \mathrm{~m}^{3} / \mathrm{s}$.

Key Concepts

Friction Factor

The friction factor is a key variable in determining pressure losses in pipe flows and depends on the Reynolds number and the relative roughness of the pipe’s interior surface. For laminar flows, it has a simple analytical expression, whereas turbulent flows often require empirical correlations or charts, such as the Moody chart, to estimate it accurately.

Darcy-Weisbach Equation

This equation provides a means to calculate the head loss or pressure drop due to friction in a pipe. It relates the pressure drop to parameters such as fluid velocity, pipe length, diameter, and the friction factor, as well as the density of the fluid. This equation is widely used in both laminar and turbulent flow conditions and is central to the analysis of viscous friction losses in pipe flow.

Continuity and Flow Rate

This principle relates the volumetric flow rate to the fluid velocity and the cross-sectional area of the pipe. It is essential for determining the velocity profile in the pipe, which is subsequently used in the calculation of friction losses and pressure drop in the system.

Reynolds Number

The Reynolds number is a dimensionless quantity that characterizes the flow regime within the pipe, indicating whether the flow is laminar or turbulent. It is calculated using fluid properties like density and viscosity, as well as the characteristic length and velocity. The value of the Reynolds number helps determine the appropriate friction factor and pressure loss calculation method.

Pressure Drop in Pipe Flow

This concept involves understanding how friction between a flowing fluid and the inner walls of a pipe causes a loss of pressure along the length of the pipe. The pressure drop is influenced by factors such as the fluid's viscosity, the pipe’s geometry, and the flow conditions. It is a fundamental consideration in fluid mechanics as it affects the design and functioning of piping systems.

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