Fluid mechanics problem about selecting pump

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vaandb_pipefrictionformulas.pptx

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Southern Methodist University

Bobby B. Lyle School of Engineering

CEE 2342/ME 2342 Fluid Mechanics

Roger O. Dickey, Ph.D., P.E.

V. STEADY PIPE FLOW

A. Pipe Friction Formulas

B. Hydraulic and Energy Grade Lines

Reading Assignment:

Chapter 3 Elementary Fluid Dynamics …

Section 3.7 - The Energy Line and the Hydraulic Grade Line, pp. 131-133

A. Pipe Friction Formulas

Empirical pipe friction formulas have been developed for specific fluids flowing through a selected range of pipe sizes and materials. This simplifies friction loss calculations by eliminating the need to determine Darcy-Weisbach friction factors.

In the U.S., the Hazen-Williams Formula is commonly used for the turbulent flow of water at normal environmental temperatures through circular pipes with diameters in the range of 2 inches to 6 ft. This formula is extensively used for design and evaluation of water distribution piping networks.

In USC units, the Hazen-Williams Formula is,

This equation holds only for the following units,

Velocity, V (ft/sec)

Hydraulic Radius, Rh (ft)

Friction Slope, Sf (ft/ft)

In SI units, the Hazen-Williams Formula is,

This equation holds only for the following units,

Velocity, V (m/sec)

Hydraulic Radius, Rh (m)

Friction Slope, Sf (m/m)

Multiply both sides of the equation by cross-sectional area, A, and substitute discharge, Q, for (VA) on the left-hand side. Also, for circular conduits flowing full, the hydraulic radius is Rh=D/4. Substituting D/4 for Rh , inserting appropriate conversion factors, and simplifying yields the Hazen-Williams Equation in terms of discharge as a function of pipe diameter:

In USC units, the Hazen-Williams Formula in terms of discharge is,

This equation holds only for the following units,

Discharge, Q (gpm)

Pipe Diameter, D (in)

Friction Slope, Sf (ft/ft)

In SI units, the Hazen-Williams Formula in terms of discharge is,

This equation holds only for the following units,

Q (m3/sec)

D (m)

Sf (m/m)

The Hazen-Williams Coefficient, C , depends on the roughness of the pipe. The higher the C value the smoother the pipe,

C < 100  Very rough pipe

C = 100 typical design value

C  140  Smooth pipe

Tables of C values are widely available for the common materials used for commercial pipe, as shown in the following table:

Typical Values of C

Pipe Material C

FE Supplied-Reference Handbook, 8th Ed., 2011 – p. 161

The Hazen-Williams Formula can be rearranged to determine the friction slope, Sf , i.e., pipe friction loss per unit length of pipe:

Only for

USC Units

Only for

SI Units

The friction loss, hf , for a given length of pipe, L, is then computed by rearranging the definition of friction slope Sf ,

Multiply the previous friction slope equations by L, use C = 100 as a reference value, and simplify to yield convenient equations for friction loss, hf :

This equation holds only for the following units,

Friction Loss, hf (ft)

Pipe Length, L (ft)

Discharge, Q (gpm)

Pipe Diameter, D (in)

Only for

USC Units

Only for

SI Units

This equation holds only for the following units,

Friction Loss, hf (m)

Pipe Length, L (m)

Discharge, Q (m3/sec)

Pipe Diameter, D (m)

Refer to Handouts – V.A. Hazen-Williams Examples for applications of the Hazen-Williams Equation.

B. Hydraulic and Energy Grade Lines

The Hydraulic Grade Line (HGL) and Energy Grade Line (EGL) are useful concepts for visualizing pipe flow problems.

The HGL is a plot of the piezometric head as the ordinate, against length along the pipe as the abscissa.

Each point along the HGL is the elevation to which the fluid would rise in a piezometer, located at that point along the pipe.

The EGL is a plot of the total available mechanical energy as the ordinate, against length along the pipe as the abscissa.

By definition, the EGL is always above the HGL by an amount .

The slope of the EGL is the friction slope, Sf , i.e., the friction loss per unit length along a pipe,

Elevation Datum

Distance

Energy

Exit

Loss

Entrance

Loss

Valve

Loss

Valve

HGL

EGL

HGL

EGL

Exit

Loss

Entrance

Loss

Reducer

Loss

Increaser

Loss

Pipe#1

Pipe#2

Pipe#3

Exit

Loss

Entrance

Loss

Pump

HGL

EGL

Pump Energy Input, hP

Static Head, z

318

849

281

278

281

278

8655

100

002083

8655

100

002131