Water llows steadily in a 125 -mm-diameter cast-iron pipe 150 m long. The pressure drop between

step 1 In this question we have to find flow rate of the flow and for this system the energy equation c

Water llows steadily in a 125 -mm-diameter cast-iron pipe...

Water llows steadily in a 125 -mm-diameter cast-iron pipe $150 \mathrm{m}$ long. The pressure drop between sections (1) and (2) is $150 \mathrm{kPa}$, and section (2) is located $15 \mathrm{m}$ above section
(1). Find the volume flow rate.

Key Concepts

Continuity Equation

This principle states that the mass flow rate must remain constant from one cross-section of a pipe to another for incompressible fluids like water. It relates the velocity of the fluid with the cross?sectional area to determine the volumetric flow rate.

Bernoulli’s Equation

Bernoulli’s Equation establishes a relationship between the pressure, velocity, and elevation head along a streamline in steady, incompressible flow. In pipe flow problems, it is used to relate the pressure drop, elevation change, and kinetic energy of the fluid, accounting for energy losses.

Darcy-Weisbach Equation

This equation quantifies the head loss due to friction along a length of pipe. It expresses the pressure drop as a function of flow velocity, pipe diameter, friction factor, and pipe length, and is essential for calculating the losses that must be overcome to sustain the flow.

Friction Factor

The friction factor is a dimensionless parameter that characterizes the resistance to flow within a pipe due to friction. It depends on the flow regime (laminar or turbulent), which is determined by the Reynolds number, and on the roughness of the pipe’s interior surface.

Reynolds Number

The Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It helps determine whether the flow in the pipe is laminar, transitional, or turbulent, which in turn influences the calculation of the friction factor and subsequently the head losses.

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