Thermodynamic Analysis

Section 5: Previous sections have addressed the tools of thermodynamic analysis. The attempt here is to treat every thermodynamic consideration with a consistent method. THERMO Spoken Here! was written to teach the method of thermodynamic analysis.

5.00  Thermodynamic Analysis

The systems of engineering analysis (mechanical systems, electrical, thermal and all others) consist of matter. Events of matter (as an event in action, an event anticipated or some event observed) are marked by the change (or non-change) of some (or none) of the system physical properties. There are many physical properties. Basic thermodynamics addresses the three basic properties: mass, momentum and energy.

5.01 Mass Equation

All engineering systems consist of matter the simplest property of which is mass. There is a general equation that "accounts" for system mass and all manners of its behavior (the system being correctly specified, of course). Logically we name that system equation after its property, the Mass Equation. The Mass Equation is an implicit, first order, differential equation with system mass as the dependent variable and time as the independent variable. This form is often called the rate-form. The equation has two types of terms, each potentially time dependent.

trans-Alaska Pipeline

Initially some 800,000 barrels of oil per day were pumped 800 miles from Prudehome Bay to Valdez where it is loaded into tankers. At a location in the pipeline, a gage measures the average velocity of the flow of oil passing through that measurement section of the four-foot diameter pipe. What reading of "average speed of flow" is expected?

5.02 System Perspectives

System is a mental construct, in each case it is an selected perspective, that is a biased approach. System is something in your head - not real. System incorporates the aspects of reality the user, the observer believes important. "What, precisely, is the system? What is relevant to the "system events," and how is it relevant?" There is rarely agreement. And when there is agreement; it is for trivial, called "classical" situations.

Dig Suez

The Suez Canal was dug across 40 miles of desert by a team of dredges. The canal initiated in a lake at its north end. It was "dug" by pumping a water-saturated sand mix (slurry) from the canal to a bank some half mile away. The average rate of sand removed by the digging machines was six million cubic feet per month. The sketch shows an average profile of the canal.
Estimate the years required to complete the digging of the canal.

Linear Valve

The supply of water to an empty tank is controlled by a valve which is initially closed. While opening the valve, the flow of water into the tank increases linearly. To open the valve completely requires two minutes and when the valve is "full-open" one cubic foot per second of water flows into the tank. The time required to close the valve completely is also two minutes.

Calculate the least time required to fill the tank and the overflow that will happen.

5.03 Leibnitz's Calculus

Beginning level systems of physics and mechanics are typically some solid, or statically constrained liquid or gas. Motions of systems that are, and remain solid or constrained, are easier studies than are motions of liquids and gases in general. Here, beginning with that simple vantage of matter, a technique of calculus is explained later to be used to describe more complicated motion of matter - motion of liquids and gases.

Derivative of an Integral with a Variable Limit:

Given:     (1) 1 then:      (2)1

5.04 Linear Mass Equation

When mass is selected (as a specific quantity and identity) that mass occupies space. The mass has what is called a "material boundary." One perspective of "conservation of mass," is that... more later! is Mass is conserved in a "material" perspective in "its" material space, meaning "the space of it (it being the original and constant identities) for all time and change. Mass stays in the space it occupies until physics decides it should move to occupy its next space - conserved in such events is a loose idea of "conserved."

Pipe Pig

When oil refinery operations change it is common that the previous product of a pipe is cleared of the previous product so the new product can pass through.

To clean a pipe a tight-fitting rubber plug, called a "pig" is placed in one end of the pipe then using compressed nitrogen it is forced through the pipe and into the holding tank. The plug pushes the previous product out, leaving the pipe clean.

Boost Pump

The schematic shows a piston/cylinder component of a hydraulic circuit. Normally the circuit operates at low-pressure. The piston is motionless and the cylinder contains its maximum volume of fluid. In this condition, hydraulic fluid pumped to the task bypasses the cylinder. Periodically, when extra "oomph" is needed, an electrical signal shuts the one-way valve and activates the motor to drive the piston to the right.

Freeze–Dried Rattlesnakes

The Bible says "snakes are evil." Conse­quently some people kill every snake they possibly can. One business sells dead snakes.

Rattlesnakes are suf­focated then, while flexible, a stiff wire is shoved through the corpse, length-wise from rattles to fangs. The wire is bent supporting the dead snake in a threatening "poised-to-strike," pose. Next the snake is frozen solid (-20°C) then placed inside a sealed chamber equipped with a vacuum pump. With prolonged pumping of first air, then air annd ater vapor, (a great while later) all of the water in the snake's body is pumped out, leaving a preserved rattlesnake trophy.

Civil Rights Memorial

This mem­orial in Montgomery, Alabama was designed by Maya Lin to honor the Civil Rights movement and some 40 persons who were murdered because they believed in equal rights for all. The names of those killed are engraved, aligned radially, around the circular edge of a massive, flat, granite stone. Water (pumped from below) rises steadily near the center of the stone, wells upward with speed, then spreads and calms as it flows outward to pass over the names of the dead. The water then wraps, without a ripple, over the rounded edge in a circular waterfall.

Expansion Flow

The sketch depicts water flowing from the left to the right without friction (we assume) through a horizontal pipe. A fixed "origin" is notated. Left of the origin the pipe diameter is d. An expansion is located at X = 0. The pipe dimeter thereafter is D. Suppose at the instant, t = t*, a point in the flow at X = XL(t*) is marked and observed to have the velocity vL(t*).

Prove the velocity of the water at X = XR(t*) is equal to (AL/AR)vL(t*).

Depth of Wine

The sketch shows an open-top cask that contains wine initially having a depth of four feet. At the start of the party (at time, t = 0+) wine is steadily released steadily from the overhead cask by abruptly removing the bung. Assume the speed of the flow of wine to be predicted by Torricelli's in Theorem:

(1) 1

As wine flowed into their flagons, some guests realized the decreasing depth of wine in the cask, H(t), was. in a way, a measure or indication of how long the party would last. Use calculus to determine if the moment half the wine is consumed corresponds to the time being one half the duration of the party.

Extruded Rod

Aluminum exits from an extrusion die at constant speed of 2 centimeters per second and a cross-sectional area of 3 square centimeters. Once the extrusion is established, a cutter actuates regularly to chop the exiting aluminum in lengths that have a mass equal to 100 grams. The sketch shows the process at the instant (t = 0+) a section was cut. That is:

Calculate the time lapse between each cut.

5.05 Momentum Equation

The model BODY is useful but limited. Thermodynamic systems don't just displace; they deform, grow, contract and flow. Extension of Newton's Second Law of Motion is our objective. When mass enters a system, it does so with a velocity, hence as mass enters, so also does momentum. It stands to reason a system equation admitting momentum crossing the system boundary would have momentum transfer terms. The mass equation and momentum equation are used together for systems with flowing mass.

Reaction of a Jet

The sketch shows a jet of water that issues from a nozzle. The stream, in an 0XY plane arrives tangent to the beginning edge of a blade that has a 90-degree blade angle. In this beginning level analysis we assume the water does not splatter and that it leaves the blade having the same speed as when it entered.

Calculate the force exerted on the block by the jet.

Jet-ski Static Pull

Two boys bought a high performance carburetor kit for their jet ski. They devised a test to evaluate the improvement. The sketch shows the machine running full-power but restrained by a cable from it to a dock. They made part of the cable include a spring scale. Use the data provided in the sketch.

Refill the Pool

Suppose you noticed the water level of your neighbor's swimming pool to be about 6 inches low. You inform him of the fact whereupon he directs a garden hose into the pool and turns it on. The pool has vertical sides and measures 15 by 36 feet.

The sketch shows the geometry of this "pool filling" event. For a moment the two of you watch the water flowing into the pool. Then, knowing you are an engineer, the neighbor asks: "When should I return and turn the water off?"


Pitot-Static Gage

Air moves with uniform velocity (section [B]) through a pipe. Some of that air headed directly for the projecting, tube-end of the gage, is decelerated ahead of the tube then comes nearly to rest, momentarily, just ahead of the tube opening, [A]. The event just described is called "stagnation of the flow." The kinetic energy of the flow changes into an increased pressure of the air at the tip of the gage. This pressure difference created is important information.

Where Water Jets Collide

The sketch shows a reservoir of water restrained by a wall. The wall has two openings, one above the other. For the instant shown, jets of water that issue from the holes intersect at a distance, L, from the tank wall. Assume the flow frictionless, the speed of each jet of water issuing from the wall outlet is given by Torricelli's Theorem. Show intersection of streams occurs at distance: L = 2 (H1 H2)1/2.

P-51 Mustang

On strafing runs WWII P-51 Mustangs often fired bursts of 1000 rounds from its six - 50 caliber machine guns. These streams of "fired lead" changed the air speed of the Mustang. This calculation will include some guess-work and approximation.
Calculate the P-51's change of air speed after it fires a burst of 1000 rounds.

5.06 Energy Equation

Vector multiplication of Newton's 2'nd Law (with a BODY as system) produced the first and simplest energy equation. Two forms of energy were identified and specified in terms of mass and the outwardly observable properties position, displacement and velocity. Work and/or equilibration were recognized as mechanisms of energy change. The basic energy equation was extended to apply to a substance (collection of Bodies). Here we review the basic equations then extend the equation to apply to a fluid that flows and might experience temperature change.

There are two water tanks connected by
a pipe with a closed valve. One tank is full,
the other is empty. The valve constrains the water.

Water Seeks its Level

The waters of Earth exist predominantly as liquid. Where liquid water is found it resides with its surface flat and tangential to Earth. Furthermore the surface is as physically low, or close to Earth as possible - subject to constraints that contain it. This example considers an amount of water initially constrained within a tank. The "event" initiates when the constraint is removed. The water, freed from the constraint flows toward Earth until a new "lesser" constraint arises. At the least constraint, water becomes part of the sea.

Gear Pump

The gear pump of a running engine receives oil at atmospheric pressure from the oil pan. Power passes from the engine through a belt-driven pulley to the shaft of the "driver gear." As the driver gear rotates, it forces the "driven gear" to rotate. Supply oil fills the spaces or "pockets" between the gear teeth of both gears. As the gears turn these "pockets" of oil are forced around the outer perimeter of the pump housing to exit at high pressure.

What ideal, steady mass rate of oil does the pump deliver?

Aquarium Turbines

Some background about aquarium pumps is needed. An aquarium pump and filter are shown in typical operation. Water, originally at the surface in the filter box (1) passes upward through the pump to jet into the aquarium with properties; (2). Water of the aquarium returns to the filter box by action of a siphon (3).

Calculate the least wattage of the pump.

NOT a "Cool Idea"

In sweltering summer heat, outdoor pools feel just like hot tubs. It's silly, but some pool owners try to "beat the heat" by dropping hundreds of pounds of ice into their pools. On the day of his daughter's wedding, an architect had 800 pounds of ice dumped into his pool which was completely full of water. In about an hour all of the ice had melted and the water in the pool was still unpleasantly warm. The architect wondered "What went wrong?"

Most of all, the Orca needs to be calm (sedated).
Next, near freezing water is a must.
Shipping Maeku

A killer whale captured off Japan is to be shipped air-freight to Miami in a container. To travel, Maeku will float in water, sedated, and harnessed to the sides of his aquarium. During the 48 hour flight,dry ice (solid carbon dioxide), will be dumped steadily into the aquarium to maintain its water at 5°C.

Instant Hot Water

The sketch shows a wall-mounted, electric-powered water heater that operated "on demand." There is no hot water tank. When the temperature control is switched, the device delivers water as shown in the promotional sketch.

Calculate the least electrical power required?

Pipe Line Flow

The sketch shows a section of a pipeline. Oil flows through the pipe steadily. Two sections (planes that cut through the pipe) are identified. Take the system to be the oil contained within the pipe between the "in" and "out" planes. Masses of oil flow across these planes.

What does the energy equation say about the flow of this physical situation?

Torricelli's Theorem

A reservoir of water extends a great distance to the left. The waters are constrained by banks, one close to us, one at a distance into the page. To the right the water is constrained by the left face of a dam. Near the base of the dam is a pipe with a closed valve. Question: When the valve is opened, what maximum exiting velocity of water would happen?

Scrapped-Surface Heat Exchanger

This device is used to "slush-freeze" concentrated orange juice. The juice is pumped through the inner annulus. A shaft passes the length of that tube with a spiral scraper attached. As ammonia passes through the outer annulus it causes the juice to freeze to the inside wall of its path. The scraper, rotated by a motor, forces the liquid/solid concentrate to exit upper right. Calculate the least steady mass rate of ammonia required by the device.

Cardiac Horsepower

At rest, your heart causes about 5 liters of blood per minute to circulate to your toes and back and elsewhere. The flow returning to the heart enters the vena cava at low velocity, with an average pressure of 10 millimeters of mercury. Your heart pumps your blood twice. First it pushes blood into your lungs. That heart-exiting flow enters the pulmonary artery at about 30 mm Hg. Returning from the lungs, oxygenated blood flows into the heart at a pressure of about 10 mm Hg. Then the heart routes the blood into the aorta (100 mm Hg) to flow back to your toes and other important (at rest) places. Estimate the average horsepower of a human heart at rest.

Niagara Power Inc.

Water that flows down the Niagara River passes over the spectacular Niagara Falls (partly in Canada, partly in the United States). A great volume of water (15 million cubic feet per minute) fall 167 feet from the escapement headed to Lake Erie.

Suppose "upstream" were dammed so the entire elevation change from the surface of Lake Erie to the surface of Lake Ontario could be used as massive hydroelectric power facility.

Tomato Juice

This juice is easily damaged by high temperature. Consequently its concentration is accomplished with modest heating by hot water in a heat exchanger followed by extraction of water from the juice by action of a vane pump that maintains a low pressure over the juice and ejects water vapor from it in a separator.

The process has two flow streams. The hot water simply enters (is cooled as the juice is heated) and exits. The other stream, juice, enters, is warmed then exits partly as concentrate and partly as vapor exhausted by the vane pump. Use the information of the drawing.

Calculate the mass rate of water that exits through the vane pump as water vapor.

ZULIA ~ Side-Casting Dredge

The shipping channel from the Caribbean Sea to the port of Caracas, Venezuela, passes through a long pond-like expanse of water called Lake Maricaibo. Since the water is too shallow for commercial shipping, the side-casting dredge, ZULIA, must dredge constantly and arduously to maintain the shipping channel.

In operation, its diesel powered pumps dredge a slurry of water and mud from the bottom of the channel and side-cast it the length of its 400 foot boom. Day by day, years pass as ZULIA toils to ever-restore the ever-filling channel.

Calculate the least pumping horsepower of the side-casting dredge.

Water Pumped Vertically

Displays of water-and-light at hotels in Las Vegas require complex piping, pumping and lighting systems. The photo shows the Bellagio water display in operation. Learn a little about such cosmetic water displays.

Light Bulb Efficiency

As a science project, students decided to evaluate the efficiency of 100-watt light bulbs. They defined "bulb efficiency" to be the visible energy produced by the bulb divided by the power expended. When a light bulb is powered, it attains steady usage of power and steady temperatures of operation nearly immediately. The tungsten filament becomes incandescent and the glass globe of the bulb becomes hot.