For a given volume flow rate and piping system, will the pressure loss be greater for hot water

step 1 Now we will apply the energy equation in flow through pipe. Energy equation. Energy equation thr

For a given volume flow rate and piping system, will the...

Key Concepts

Fluid Properties Variation with Temperature

The viscosity and density of a fluid, such as water, change with temperature. As water heats up, its viscosity decreases, which means it flows more easily with less internal resistance. Additionally, the density slightly decreases with temperature. Both of these changes affect how the fluid behaves when moving through a piping system, influencing the pressure loss encountered along the flow path.

Darcy-Weisbach Equation

The Darcy-Weisbach equation provides a fundamental relation for calculating pressure loss in pipes by linking the frictional head loss to factors such as friction factor, pipe length, diameter, fluid velocity, and density. Since the friction factor itself is influenced by the flow regime and the fluid’s viscosity (which is temperature-dependent), this equation is central in explaining why pressure losses vary with the temperature of the water.

Reynolds Number

The Reynolds number is a dimensionless parameter that helps determine the flow regime in a pipe, whether laminar or turbulent. It depends on properties like velocity, characteristic length (such as pipe diameter), and fluid viscosity. Because viscosity decreases with temperature, the Reynolds number increases for hot water compared to cold water under the same flow conditions. This shift can lead to differences in the friction factor and, ultimately, in the pressure loss along the pipe.

Transcript

00:01 Now we will apply the energy equation in flow through pipe.

00:05 Energy equation.

00:07 Energy equation through pipe.

00:18 We can write p1 divided by row plus alpha multiplied by v1 squared by 2 plus gz1.

00:27 Gz1 multiplied by this term minus p2 divided by row plus p2 divided by row plus alph alpha 2 multiplied by v2 squared divided by 2, v2 squared divided by 2, this is alpha 1 plus gz 2, this term will be equals to net head.

00:55 So this is hl plus hl infinity.

01:03 So let this is equation number 1.

01:06 So here p1 and p2 are the pressure rate state 1 and 2.

01:09 R, the density, v1, v2 are the velocity, and z1, z2 are the datum head set at state 1 and 2.

01:15 And as the, assuming the velocity and elevation effects are negligible, so we can write v1 is equal to v2 as well as z1 is equal to z2.

01:28 Alpha is the kinetic, alpha 1 is equal to alpha 2 is equal to 1, as this is the kinetic energy correction factor.

01:35 And there is no change in kinetic energy.

01:37 Now the major head loss due to friction head loss due to friction head loss head loss due to friction due to friction can be written as head loss due to friction can be written as hl infinity hl infinity this term will be equals to f multiplied by lv squared divided by 2d flv squared divided 2d where f is the friction factor f is equal to friction factor f is equals to friction factor fricion factor fricion factor l is the length with the velocity also also we can write we can write the minor head loss in the pipe minor head loss in pipe can be written as h.

02:33 Hl minor is equals to kv squared divided by 2.

02:41 Here k is the minor...

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