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LMNO Engineering, Research, and Software, Ltd. |

Index to all Newsletters LMNO Engineering home page
email: LMNO@LMNOeng.com |

2016

August 18, 2016. Gradually Varied Flow graphical and tabular calculator

March 31, 2016. A Common Question

2015

July 19, 2015. Gas Viscosity Calculator

2014

September 8, 2014. Two Topics - mobile calculations and venturi flow meter

2013

July 22, 2013. Time to Empty a Tank

February 5, 2013. Water Velocity in a Tank at Various Heights above a Drain

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. August 18, 2016

Gradually Varied Flow (GVF) Calculator

Now with graph and table. Now mobile-device-friendly.

http://www.LMNOeng.com/Channels/gvf.php

On August 4, we loaded our newest mobile-friendly calculation. It is for gradually varied flow (GVF, which is also known as backwater flow). It is at http://www.LMNOeng.com/Channels/gvf.php. The calculation has a nice demonstration mode, so you can see graphs and tables showing water depth upstream or downstream of a barrier. In addition to water depth, it will also plot and give a table for velocity, Froude number, and top width versus distance in the demonstration mode. In addition to the graph and table, numbers for depth, velocity, Froude number, and other parameters are output at any distance specified by the user.

After clicking on "Click to Calculate", links for the graph and table will appear. Clicking on the links will bring up the graph and table in new tabs. The tabular output is comma-separated, so you can copy/paste the values into a spreadsheet to make custom graphs.

As background, GVF and RVF (rapidly varied flow) are terms used to classify open channel flows - such as flow in rivers, canals, and culverts. RVF occurs over short distances such as when water flows over a weir or dam, drops off the end of a pipe, or encounters an hydraulic jump. GVF occurs over long distances such as water approaching a weir, dam, or drop-off; or following a sluice gate.

In long prismatic (constant cross-section geometry) channels, the water will attempt to reach the "normal depth" (also known as "uniform flow depth"). Normal depth is the water depth determined using Manning's equation (or Chezy's equation). How the water depth changes with distance as it approaches normal depth is called a GVF profile. A GVF profile is obtained through a computation of water depth versus distance along the channel length. A GVF computation typically involves starting at a known depth (e.g. at a dam) and making successive computations upstream using the continuity equation and energy slope in Manning's equation (rather than using the channel bottom slope). It is a numerical computation. Thus for highest accuracy, it is desirable to use small distance increments as our program does. If you have had a course in open channel flow, you might recall the different GVF profile types - such as M1, M2, M3, S1, S2, S3, etc.

Please let me know if you have any questions. Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)

LMNO Engineering, Research, and Software, Ltd.

http://www.LMNOeng.com LMNO@LMNOeng.com

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.

© 2016 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. March 31, 2016

A Common Question

The most common question I am asked is, "I know the pressure in my pipe. What is the flow rate?" That question is not simple to answer. Unless the fluid is passing through a control section, such as a choked flow section, then two pressure readings are needed. If flow is discharging downstream to the atmosphere, then you have a second known pressure (atmospheric pressure) and flow can be determined.

Alternatively, if more information is provided about the piping system, then the additional information may be sufficient to calculate the flow rate. For instance, if there is a tank upstream or downstream of the pressure reading, then the pressure in the tank can be used as the second data point and flow can be computed.

Our Liquid or Gas Pipe Design calculator (http://www.LMNOeng.com/DarcyWeisbach.php) demonstrates how elevation change, pressure change, and/or pumping can drive the flow of a liquid or gas. In the calculation, you can enter pipe diameter, length, loss coefficients for fittings, pressure change, and elevation change, and the calculation will compute the pipe flow rate. Alternatively, you can enter flow rate, and the calculation will compute the other parameters.

Please let me know if you have any questions. Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)

LMNO Engineering, Research, and Software, Ltd.

http://www.LMNOeng.com LMNO@LMNOeng.com

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.

© 2016 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. July 19, 2015

Gas Viscosity Calculator

http://www.LMNOeng.com/Flow/GasViscosity.php

Our most popular calculator is our free gas viscosity calculator. Gas viscosity is used to compute pressure drop when gases flow through pipes. Our calculator computes gas viscosity as a function of temperature for air, natural gas, hydrocarbon vapor, ammonia, carbon dioxide, carbon monoxide, hydrogen, nitrogen, and sulfur dioxide. Dynamic viscosity is primarily a function of temperature, rather than pressure, for pressures up to 500 psi (34.5 bar) (Crane, 1988).

Our gas viscosity calculator is based on the methodology in Crane (1988) and the CRC Handbook of Chemistry and Physics (1984). The viscosity of many gases can be computed by the Sutherland formula shown on the web page. For natural gases with various specific gravities, the Sutherland formula does not apply. In this case, we have taken data points from graphs in very small intervals and input them into our calculation. Then, the calculation interpolates linearly between the points.

In addition to selecting the gas of interest, the calculation allows you to choose the temperature units of Celsius, Kelvin, Fahrenheit, or Rankine and the dynamic viscosity units of lb-s/ft^{2}, N-s/m^{2}, poise, and centipoise. Note that 1 poise = 0.1 N-s/m^{2} and 1 centipoise = 0.001 N-s/m^{2} (per http://www.LMNOeng.com/units.php).

Please see our full list of 80 calculations for pressure pipe flow, choked gas flow, water hammer, open channel flow, hydrology, groundwater, drag force, and tank sizing at http://www.LMNOeng.com.

Please let me know if you have any questions. Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)

LMNO Engineering, Research, and Software, Ltd.

http://www.LMNOeng.com LMNO@LMNOeng.com

References:

Chemical Rubber Company (CRC). 1984. CRC Handbook of Chemistry and Physics. Weast, Robert C., editor. 65th edition. CRC

Press, Inc. Boca Raton, Florida. USA.

Crane Company. 1988. Flow of fluids through valves, fittings, and pipe. Technical Paper No. 410 (TP 410).

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.

© 2015 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. September 8, 2014

Two Topics:

Mobile-Device-Friendly Calculations

Venturi Flow Meter Calculation: http://www.LMNOeng.com/venturi.php

My last newsletter was on July 22, 2013. We are in the process of converting our software from the Java language to the PHP language. Having our programs in PHP will enable them to be viewable on mobile devices. They will also more readily run on computers since you will not need to download any additional software from the web. Currently, you need to download the Java Runtime Environment to run our Java applets. We have converted 29 programs so far. Please see our home page http://www.LMNOeng.com for a list of programs (the PHP programs have a + next to them).

The most recent program that we converted to PHP is our venturi flow meter calculator. A venturi flow meter is a differential pressure flow meter. Differential pressure is the difference in pressure between a high pressure upstream tap and a low pressure tap at the throat of the venturi. Knowing the differential pressure, upstream diameter, throat diameter, and fluid density and viscosity, the flow rate can be computed.

Standards have been written by various professional organizations (e.g. International Organization of Standards and American Society of Mechanical Engineers) so that a venturi flow meter manufactured to conform to the standard can be used "out of the box" without any calibration. Venturi flow meters have the advantage over nozzle and orifice meters (also differential pressure flow meters) because venturi meters result in a lower overall pressure loss through the device. Our venturi flow meter calculation allows you to enter a variety of units and solve for flow rate, differential pressure, or throat diameter.

Thank you for your interest in the LMNO Engineering newsletter,

Ken Edwards, Ph.D., P.E. (Owner/Engineer)

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.

© 2014 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. July 22, 2013

Time to Empty a Tank

http://www.LMNOeng.com/Tank/TankTime.htm

We are sometimes asked how long it will take to empty a tank or drain a pond. Our
calculation to compute the time for the liquid level in a tank to drop can be found at http://www.LMNOeng.com/Tank/TankTime.htm
. The calculation uses the equation:

t = A/(a C) (H_{i}^{0.5} - H_{f}^{0.5}) (2/g)^{0.5}

where (sample units are shown in parentheses):

a = Orifice area (m^{2}).

A = Tank cross-sectional area (looking down on the tank, m^{2}).

C = Orifice discharge coefficient.

g = Acceleration due to gravity (9.8066 m/s^{2}).

H_{i} = Initial liquid depth above orifice centerline (m).

H_{f} = Final liquid depth above orifice centerline (m).

t = Time for liquid to drop from H_{i} to H_{f} (sec).

For instance, if C=0.6, Orifice diameter=0.01 m, Tank diameter=0.5 m, H_{i}=3 m, H_{f}=0.2
m, then:

a = π d^{2} /4 = pi (0.01m)^{2} /4 = 7.854e-5 m^{2}

A = π D^{2} /4 = pi (0.5m)^{2} /4 = 0.1963 m^{2}

t = (0.1963 m^{2}) / [(7.854e-5 m^{2})(0.6)] [(3
m)^{0.5} - (0.2 m)^{0.5}] (2/9.8066 m/s^{2})^{0.5}

= 2417 sec = 40.3 minutes

In addition to time, the calculation can compute one of the other variables - orifice
coefficient, initial depth, final depth, tank area (or diameter), or orifice area (or
diameter). Our calculation allows you to select a variety of units.

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.

© 2013 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. February 5, 2013

Water Velocity in a Tank at Various Heights above a Drain

Consider a tank (or swimming pool) where there is a drain (orifice) on the flat bottom of the tank which discharges freely to atmospheric pressure as shown in the figure. If the diameter of the opening is D=0.5 ft and the water depth remains constant at H=20 ft, then what are the pressure and velocity of the flowing water at various heights y directly above the orifice?

The orifice discharge velocity V_{o} is: V_{o} = (2gH)^{0.5}
= [(2)(32.2 ft/s^{2})(20 ft)]^{0.5} = 35.89 ft/s where g =
acceleration due to gravity = 32.2 ft/s^{2}

The orifice area A_{o} is: A_{o} = π D^{2} / 4 = π
(0.5 ft)^{2} / 4 = 0.1963 ft^{2} where π = 3.14159....

The flow rate Q out of the orifice is: Q = C A_{o} V_{o} =
(0.6)(0.1963 ft^{2})(35.89 ft/s) = 4.228 ft^{3}/s where C is the
orifice discharge coefficient, typically 0.6 but depends on its rounded-ness.

The approximate streamline paths are shown in the following figure.

Think of the streamlines in three dimensions, sort of like a funnel. To determine the
velocity at heights y directly above the orifice, we need to determine an area
distribution. An approximation is to use the surface area of a hemisphere. The surface
area of a sphere is 4 π r^{2} where r is the sphere radius. The surface area of a
hemisphere is then 2 π r^{2}. Thus, the area distribution as a function of height
y is: A(y) = 2 π y^{2}

Then the velocity V(y) at heights above the orifice is (from conservation of mass for a constant density fluid like water): V(y) = Q / A(y)

The pressure P(y) at heights y above the orifice is computed from the Bernoulli
equation: P(y) = w { [V_{o}^{2} - V(y)^{2}] / (2g) - y}
where w = weight density of water = 62.4 lb/ft^{3}

A sample calculation at y = 2 ft:

A(y=2 ft) = 2 π y^{2} = 2 π (2 ft)^{2} = 25.13 ft^{2}

V(y=2 ft) = Q / A(y) = (4.228 ft^{3}/s) / (25.13 ft^{2}) = 0.1682 ft/s

P(y=2 ft) = w { [V_{o}^{2} - V(y)^{2}] / (2g) - y}= (62.4 lb/ft^{3})
{ [(35.89 ft/s)^{2} - (0.1682 ft/s)^{2}] / [(2)(32.2 ft/s^{2})] -
2 ft } = 1123 lb/ft^{2} = 7.800 lb/in^{2} = 7.800 psi

A table can be developed:

y | V(y) | P(y) |

(ft) | (ft/s) | (psi) |

0.5 | 2.69 | 8.40 |

1 | 0.673 | 8.23 |

2 | 0.168 | 7.80 |

5 | 0.0269 | 6.50 |

10 | 0.00673 | 4.33 |

15 | 0.00299 | 2.17 |

20 | 0.00168 | 0 |

As y increases, velocity decreases and pressure approaches hydrostatic pressure, w(H-y)
in lb/ft^{2} or w(H-y)/144 in psi.

Thank you for your interest in the LMNO Engineering newsletter and the fluid flow
calculations website http://www.LMNOeng.com,

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.

© 2013 LMNO Engineering, Research, and Software, Ltd.

**© 2013-2016 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