Basic Thermodynamics ~ J. Pohl © www.THERMOspokenhere.com (218-E365)

ZULIA ~ Side-Casting Dredge

The shipping channel leading from the Caribbean Sea to the port of Caracas, Venezuela, passes across a long pond-like expanse of water called Lake Maricaibo. The water being too shallow for commercial shipping, the side-casting dredge, ZULIA, must dredge constant 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.

Estimate the least pumping horsepower of the side-casting dredge.
♦  We assume the state of the dredge to be operating in a steady manner, that it is and has been running without problems for a few weeks, say. We take the lake water that passes through the dredge as the system material.

It is clear where this water exits our system - at the end of the side-casting boom. As for the entrance of our system, the schematic shows the letter, A, with a "free-surface" notation (an inverted Δ) beside it. Our choice is to set the datum for potential energy to be zero at that place, at the elevation of the surface of the water near A. Our entrance, how we will model the "in" of this system was described in the second proof of of a previous writing ~ Torricelli's Theorem.

Mass Equation  First we address the mass equation for the system and its event. The notation, discrete summation Σ is used with massesin for the moment. But there being a single exit at the end of the casting boom, no summation symbol is needed there.

(1)♦  dm/dt is zero because no mass accumulates
within the pumps and piping.

The term, dm/dt, represents the change of mass of water within, that is an accumulation within the pumps and piping. There is none: this term equals zero. More can be said about the exiting flow stream. However, not knowing the density of the mud/water slurry that is pumped; we assume its density to be that of water.

(2)♦  Knowing the density of water and the volumetric rate yields
the mass rate through the system.

Knowing the density of water and the volumetric rate yields the mass rate through the system. The volumetric flow past a plane equals the average velocity of the flow times the flow area. This fact yields the average velocity of the water at the system exit.

(3) ♦  The exiting average velocity of the slurry.

Energy Equation  The flow of this fluid is steady and it (water) is incompressible. The steady energy equation applies:

4 (4)♦  As a first calculation, frictional losses are assumed equal to zero.

The entering and leaving mass rates are equal. Pressures "in" and "out" are atmospheric. To re-group on like terms is logical.

5 (5)♦  The pressure of the atmosphere has nothing to do with the pump power required.
Just one more line of algebra.
(6)♦  The minus signs denote energy the leaves the system.

Numbers can be applied to the above energy equation. Hopefully we have are enough numbers for a solution. Note: Please resist the urge to "do algebra" on this equation. It has dignity, has meaning that is something upon algebraic rearrangement.

(7) ♦  An equation contains a solution once it is ALL numbers, with only one unknown remaining, represented by its symbol.
(8) ♦  Do the algebra now. Apply the necessary units.

The answer we obtain is ludicrous. There are inexpensive motorcycles that have 260 horsepower engines. This being a beginning level discussion, we have assumed friction to be nonexistent. Friction is never zero; it is BIG. To include its effects requires advanced study and/or expensive experimentation.