Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

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7 Spaces Of Interest - Overview

Triadic Unit Mesh

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COHN - Natures Engineering Of The Human Body

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Differential Calculus

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Painting

Water Pressure And Flow Of Water In Pipes

The quantity of water that flows through a pipe depends primarily on the *head*, pipe diameter, nature of interior surface and the number and shape of the bends.
**(a)** Consider figure 28.1. Indicate the *water head*.
**(b)** How is the *water head* calculated if it is mechanically established by *pumping*?
**(c)** A pipe line, 1/2 a mile long, 12 inches in diameter, discharges water under a head of 100 feet. Find the velocity and quantity of discharge .
**(d)** What length of straight pipe should compensate for the loss of head in pipe due to a right angle bend in pipe.

**The strings**:
S_{7}P_{3}A_{32} (force-push).
**The math**:

Pj Problem of Interest is of type *force* (force-push).

**(a)** Consider figure 28.1. *Water head* = h_{1} - h_{2}. In essence, the *water head* is the difference in potential energy relative to ground. That is, (h_{1} - h_{3}) - (h_{2} - h_{3}). The pressure that forces water out of the pipe is directly related to the *head* and is zero when h_{1} = h_{2}.
**(b)** *Head* = vertical distance corresponding to the mechanical pressure.

For example, 1lb/in^{2} = 2,309 ft head, and 1 foot-head = 0.433 lb/in^{2}.
**(c)** Formula in focus is:
** V = C(hD/(L +54D)) ^{1/2}** -------------(1).

This formula is an approximation with 5% to 10% accuracy.

Where V = approximate mean velocity in feet per second

C = coefficient associated with pipe diameter. A table of pipe diameters and C is usually available.

For this problem, C = 48 for pipe diameter of 1 foot.

D = Diameter of pipe in feet.

h = total head in feet

L = total length of pipe line in feet.

So, substituting in equation (1), we have:

Velocity of discharge, V = 48[(100 x 1)/(2640 + 54(1))]

Area of cross section of pipe = πr

So, Discharge = 9.233 x 0.7854 = 7.252 cubic-ft/sec.

Experiments indicate approximately, that a right angle bend has radius of 3 times the diameter of the pipe.

Formula for right angle bend:

L

So, L

Formula for valves:

L

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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