Volume 10
No. 2.  May 29, 2008. Videos of Experiment and Analysis of Water Discharging from a Tank
No. 1.  February 14, 2008. Fire Hydrant Pressure Requirement

Volume 9
No. 1.  November 13, 2007. Summary of Software

Volume 8
No. 5.  October 23, 2006. End Depth Method for Flow Measurement in Open Channels
No. 4.  August 21, 2006. Volume in Inclined Cylinder
No. 3.  May 16, 2006. Gas Flow Conversions
No. 2.  April 4, 2006.  Culvert Design
No. 1.  February 9, 2006.  Newsletter Topics

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 10, No. 2. May 29, 2008

Videos of Experiment and Analysis of Water Discharging from a Tank
http://www.LMNOeng.com/Video

We have recently made some movies of a fluid mechanics experiment and its analysis. One of the videos shows water discharging steadily from a tank through a 0.25 inch diameter orifice. The head, flowrate, horizontal trajectory, and vertical trajectory are measured.

The other two videos show how equations and the calculation at our Tank Discharge page can be used to predict the experimental results.

The basic equation for steady discharge from an orifice in terms of head is
( from http://www.LMNOeng.com/TankDischarge.htm ):

Q = C_o A (2gh)^0.5

where
A = area of orifice (ft²)
C_o = orifice coefficient = 0.61 for a sharp-edged orifice
g = acceleration of gravity = 32.174 ft/s²
h = head (ft)
Q = flowrate (i.e. discharge) out of the orifice (ft³/s)

Alternatively, to compute discharge from the trajectory:

Q = C_c A X [g/(2Y)]^0.5 

where
C_c = contraction coefficient of orifice = 0.62 for a sharp-edged orifice
X = horizontal trajectory (ft)
Y = vertical trajectory (ft)

Any other consistent set of units can be used in the equations.
Also, note that C_o = C_c C_v
where C_v = velocity coefficient = 0.98 for a sharp-edged orifice

Please let me know if you have any questions or are interested in other experiments.

Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.
(c) 2008 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 10, No. 1. February 14, 2008

Fire Hydrant Pressure Requirement

Fire hydrants may appear to be mundane pieces of equipment, having been around - in one form or another - for centuries. These fairly simple pieces of equipment can require higher main line pressures than expected in order to obtain the expected flow.

For instance, consider the case of a hydrant located on a 6-inch diameter pipe. A flow test is conducted where the 2.5-inch diameter nozzle is open and allowed to flow freely to the atmosphere.

The energy equation for an incompressible liquid is written from the 6-inch diameter pipe at the hydrant inlet to the 2.5-inch nozzle discharging to atmospheric pressure:

Z_p + P_p/S + V_p² /(2g) = Z_n + P_n/S + V_n² /(2g) + Loss/S

where (ft=feet, s=second, psi=pounds per square inch gage, psf=pounds per square ft gage, cfs = ft³/s; gage means relative to atmospheric pressure):
g = Acceleration due to gravity = 32.2 ft/s²
Loss = Friction and other losses within the hydrant, psf
P_n = Pressure at 2.5-inch nozzle discharging to the atmosphere = 0 psf
P_p = Pressure in 6-inch diameter pipe at inlet to fire hydrant, psf
S = Specific weight of water (not specific gravity) = 62.4 lb/ft³
V_n = Velocity in 2.5-inch nozzle as it discharges to the atmosphere, ft/s
V_p = Velocity in 6-inch pipe, ft/s
Z_n = Elevation of 2.5-inch nozzle, ft
Z_p= Elevation of pipe, ft

A hydrant typically is supposed to have no more than about a 5 psi pressure loss. The height of the 2.5-inch nozzle above the hydrant inlet is about 6 ft. Hydrants are often desired to have a flow of 1000 gpm. Therefore, for this case:

Z_n - Z_p = 6 ft
Loss = (5 psi)(144 in²/ft²) = 720 psf
Q = Flow = (1000 gpm)(cfs/448.8 gpm) = 2.228 cfs
D_n = Diameter of nozzle = (2.5 in)(ft/12 in) = 0.2083 ft
A_n = Nozzle area = (pi/4)(0.2083 ft)² = 0.03409 ft²
A_p = Area of 6-inch pipe = (pi/4)(0.5 ft)² = 0.1963 ft²
V_n = Q/A_n = (2.228 cfs)/(0.03409 ft²) = 65.36 ft/s
V_p = Q/A_p = (2.228 cfs)/(0.1963 ft²) = 11.35 ft/s

Then,
V_n²/(2g) = (65.36 ft/s)² / [(2)(32.2 ft/s²)] = 66.33 ft
V_p²/(2g) = (11.35 ft/s)² / [(2)(32.2 ft/s²)] = 2.000 ft
Loss / S = (720 lb/ft²) / (62.4 lb/ft³) = 11.54 ft

Now, solve for P_p using the energy equation:

P_p/S = (Z_n - Z_p) + P_n/S + V_n²/(2g) - V_p²(2g) + Loss/S

= 6 ft + 0 ft + 66.33 ft - 2.000 ft + 11.54 ft

= 81.87 ft

Then,
P_p = (81.87 ft)(62.4 lb/ft³)(ft²/144 in²) = 35.5 psi

Thus, a pressure of 35.5 psi is required to push 1000 gpm from a 6-inch pipe through the hydrant internals, up 6 ft, and out the 2.5-inch nozzle to the atmosphere.

Alternatively, if the 4.5-inch nozzle was flowing to the atmosphere (instead of the 2.5-inch nozzle), then:
A_n=(pi/4)(4.5/12 ft)² = 0.1104 ft²
V_n=(2.228 cfs)/(0.1104 ft²) = 20.17 ft/s
V_n²/(2g) = (20.17 ft/s)² / [(2)(32.2 ft/s²)] = 6.319 ft

Then,
P_p/S = 6 ft + 0 ft + 6.319 ft - 2.000 ft + 11.54 ft
= 21.9 ft

and

P_p = (21.9 ft)(62.4 lb/ft³)(ft²/144 in²) = 9.5 psi

Thus, a pressure of only 9.5 psi is required to push 1000 gpm from a 6-inch pipe through the hydrant internals, up 6 ft, and out the 4.5-inch nozzle to the atmosphere.

The difference in pressures (35.5 psi versus 9.5 psi) is attributable to the higher velocity head that must be overcome for flow out of the smaller nozzle.

One could do the calculation in reverse to compute the flow out of the 2.5-inch or 4.5-inch nozzle for a given pressure in the 6-inch pipe. Often, water systems are designed to deliver 20 psi at hydrant inlets.

The calculations assume an elevation change of 6 ft from the 6-inch pipe to the nozzle discharge and a loss of 5 psi through the hydrant. Additional loss due to the water contracting to a "vena-contracta" diameter of less than the nozzle diameter as it flows out of a nozzle was not included.

I hope that this newsletter has demonstrated the significant impact of exit nozzle velocity head on required pressure for flow out of a hydrant that is freely discharging to the atmosphere, as in a hydrant flow test.

Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)


You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2008 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 9, No. 1. November 13, 2007

Thank you for opting-in to our newsletter. It has been about a year since I sent a fluid flow newsletter. If you no longer wish to be on our list, simply respond and put "Discontinue newsletter" in the subject line. Though new people opt-in regularly, some people have been on our newsletter list for 9 years and may no longer be interested.

There are now over 60 fluid flow calculations on our website. To show our appreciation for our newsletter subscribers, please use the following free PIN number: LMNOeng (use exact capitalization). Enter the PIN at our home page http://www.LMNOeng.com . All of the calculations will be enabled until November 21, 2007.

Here is a summary of the calculations we have on our site:
Closed conduit (pressurized flow) calculations for computing flowrate, pressure drop, elevation change, pump head, or pipe diameter using the Darcy-Weisbach or Hazen-Williams method for friction losses. Hazen-Williams is primarily used for municipal water supply pipes while Darcy-Weisbach is valid for other liquids in addition to water.

Weymouth and Panhandle methods for compressible gas flow.
Pipe network calculation for up to 12 pipes and 9 nodes.
Orifice, nozzle, and venturi flowmeter calculations based on ISO and ASME standards.

Force due to a pipe bend. Discharge from a tank.

Open channel flow calculations for Manning's equation and inlet/outlet control.
Inverted siphon for piping storm water under a river.
Flumes, weirs. Hydraulic jump calculator.
Runoff and detention basin sizing. Groundwater and contaminant migration.

Volume calculators for inclined and horizontal cylinders (tanks).
Gas density, viscosity, unit conversions.

Please let me know if you have any questions. I plan to write newsletters every few months with technical information about fluid flow. Please see my past newsletters that are listed at the bottom of our home page.

Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)


You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com .

(c) 2007 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 8, No. 5. October 23, 2006

End Depth Method for Flow Measurement in Open Channels

Ever wish you could determine the discharge (Q) of water out of a culvert? Maybe you thought about using Manning's equation - but you needed to measure the slope and estimate the Manning coefficient (n). And you realized that a small error in estimating n can give a large error in Q. Maybe you found Q by measuring the time to fill a 20 liter bucket. For high flows, the time is too short to measure accurately; and larger buckets get too heavy.

The end depth method doesn't require a slope measurement or an estimation of n. It is based solely on the water depth (h) and diameter (D) of the culvert. It requires that the culvert be essentially horizontal and that the water drops off a height greater than h.

We have end depth calculations for circular culverts, rectangular channels, and triangular channels that have sudden drop-offs (like a waterfall). The rectangular and triangular channel calculations are fully functional without paying our registration fee. You can see the rectangular channel calculation at http://www.LMNOeng.com/Waterfall/waterfall.htm .

Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)

LMNO Engineering's previous newsletters can be viewed at http://www.LMNOeng.com/Newsletters/newsletter8.htm  


You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com .

(c) 2006 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 8, No. 4. August 21, 2006

Partially Full Inclined Cylinder Volume Calculation
http://www.LMNOeng.com/Volume/InclinedCyl.htm

Last month we completed a calculation that many visitors have requested over the past few years. It computes the volume of liquid contained in a partially full inclined cylinder. It can be used for computing the oil volume in a storage tank that is not horizontal. Or the volume of water in a pipeline that is sloped. The user enters the cylinder diameter, length, and angle from horizontal.

The calculation allows you to enter the liquid depth measurement several ways:
1. Vertical distance from bottom of tank to liquid surface.
2. Vertical distance from top of tank down to liquid surface.
3. Distance from bottom of tank to liquid surface measured perpendicular to bottom of tank.
4. Distance from top of tank to liquid surface measured perpendicular to top of tank.

Since the cylinder is at an angle, the user must also indicate how far from the downstream edge of the tank the depth measurement is made.

A full description of the governing equations, inputs, and outputs are shown on the web page http://www.LMNOeng.com/Volume/InclinedCyl.htm. If you are interested in the mass of liquid in the tank, just multiply the output volume by the liquid density.

I hope you find the calculation helpful. Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

LMNO Engineering's previous newsletters can be viewed at http://www.LMNOeng.com/Newsletters/newsletter8.htm


You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com .

(c) 2006 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 8, No. 3. May 16, 2006

Gas flow conversions
http://www.LMNOeng.com/Flow/GasFlow.htm

We have completed a new calculation called Gas Flow Conversions. There is often confusion about how gas flowrates are stated, so we developed the calculation to aid in unit conversions for gas flow. Some gas flows are expressed in mass units, like kg/s or lb/day. Sometimes, flow units are acfm, scfm, or Nm3/s, to name a few.

Mass flowrate is straightforward. It is the amount of mass flowing per unit time. Volumetric flowrates, however, are either expressed as flow at "actual conditions" or flow at "standard (or normal) conditions". Units for flow at actual flowing conditions often have the letter "a" in front of the unit.

In contrast to flow at actual conditions, flows can be expressed at standard (or normal) conditions. English units usually are prefaced with the word "standard" or letter "s" while metric units are usually prefaced with the word "normal" indicated by the letter "N" (don't confuse with the Newton unit).

Standard (or normal) flows are the volume equivalent to actual flow if the actual flow were at standard temperature and pressure. For the same mass and temperature of gas, one cubic meter of a gas at 10 atmospheres of pressure occupies much more volume when its pressure is reduced to 1 atmosphere. Think of gas in a cylinder acted on by a piston.

Please see our web page http://www.LMNOeng.com/Flow/GasFlow.htm for equations and further discussion of gas conversions.

Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

LMNO Engineering's previous newsletters can be viewed at http://www.LMNOeng.com/Newsletters/newsletter8.htm

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2006 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 8, No. 2. April 4, 2006

Culvert Design using Inlet and Outlet Control
http://www.LMNOeng.com/Pipes/hds.htm

Culverts have been utilized for thousands of years as a means to transmit water under walkways and roads. Too often, culverts are selected without sufficient thought of how much water needs to be conveyed under extreme conditions. If a culvert cannot convey all of the incoming water, then the water will flow over or around the pipe - or simply back up behind the culvert creating a pond or reservoir. If any of these conditions are unacceptable, then the proper culvert diameter and number of culverts must be selected prior to installation in order to convey all of the anticipated water through the pipe(s).

Discharge through a culvert is controlled by either inlet or outlet conditions. Inlet control means that flow through the culvert is limited by culvert entrance characteristics. Outlet control means that flow through the culvert is limited by friction between the flowing water and the culvert barrel. The term "outlet control" is a bit of a misnomer because friction along the entire length of the culvert is as important as the actual outlet condition (the tailwater depth). Inlet control most often occurs for short, smooth, or greatly downward sloping culverts. Outlet control governs for long, rough, or slightly sloping culverts. The type of control also depends on the flowrate. For a given culvert installation, inlet control may govern for a certain range of flows while outlet control may govern for other flowrates. If the flowrate is large enough, water could go over the road (or dam). In this case, our calculation automatically computes the amount of water going over the road and through each culvert, as well as the headwater depth.

Our culvert design calculation aids the designer in selecting the number of culverts and culvert diameter. It also plots headwater depth vs. discharge so that the designer can view culvert performance over a wide range of flows. Our calculation is primarily based on the methodology presented in Hydraulic Design of Highway Culverts by Normann (1985) and published by the USA Department of Transportation's Federal Highway Administration.

Please see http://www.LMNOeng.com/Pipes/hds.htm to run the calculation and to see equations, diagrams, and additional description.

Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

Reference:
Normann, J. M. 1985. Hydraulic design of highway culverts. HDS-5 (Hydraulic Design Series 5). FHWA-IP-85-15. (2005 update viewable at http://isddc.dot.gov/OLPFiles/FHWA/012545.pdf - file size is 9MB)

LMNO Engineering's previous newsletters can be viewed at http://www.LMNOeng.com/Newsletters/newsletter8.htm

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com .

(c) 2006 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Newsletter. Vol. 8, No. 1. February 9, 2006.

Newsletter Topics

Many of you have been newsletter subscribers for a long - possibly since 1998 when we started LMNO Engineering. Others are more recent newsletter subscribers. If there are any topics you would like to learn about, please let me know by emailing me at LMNO@LMNOeng.com .

Over the years, I have written newsletters regarding many aspects of fluid flow, which relate to our software. These topics have included pressurized pipe flow and flow measurement; flow of gases and liquids in pipes; networks of parallel and series pipes; orifice, nozzle, venturi flow meters; and the Bernoulli equation. I have written about open channel flow in circular pipes and trapezoidal channels; gradually varied flow profiles; inverted siphons for carrying stormwater or wastewater under roads or rivers; culvert design using inlet and outlet control; and weirs and flumes for flow measurement. There have been newsletters about watershed runoff - time of concentration, Rational equation, TR-55 method. And groundwater flow and contaminant transport.

All of the past newsletters are listed at the bottom of our home page http://www.LMNOeng.com . Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

LMNO Engineering's previous newsletters can be viewed at http://www.LMNOeng.com/Newsletters/newsletter8.htm


You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2006 LMNO Engineering, Research, and Software, Ltd.

© 2006-2008 LMNO Engineering, Research, and Software, Ltd. (All Rights Reserved)

LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd.   Athens, Ohio  USA   +1(740) 592-1890
LMNO@LMNOeng.com    http://www.LMNOeng.com