Water Pressure And Flow Of Water In Pipes

Water Pressure And Flow Of Water In Pipes
TECTechnics Classroom TECTechnics Overview

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: S₇P₃A₃₂ (force-push).

The math:
Pj Problem of Interest is of type force (force-push).

(a) Consider figure 28.1. Water head = h₁ - h₂. In essence, the water head is the difference in potential energy relative to ground. That is, (h₁ - h₃) - (h₂ - h₃). The pressure that forces water out of the pipe is directly related to the head and is zero when h₁ = h₂.

(b) Head = vertical distance corresponding to the mechanical pressure.
For example, 1lb/in² = 2,309 ft head, and 1 foot-head = 0.433 lb/in².

(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))]^1/2 = (0.037)^1/2 = 9.233 ft/sec.

Area of cross section of pipe = πr² = π(0.5)² = 0.7854 sq-ft.
So, Discharge = 9.233 x 0.7854 = 7.252 cubic-ft/sec.

(d) Loss of head due to a bend in pipe = equivalent length (L_e) of straight pipe that causes same loss in head as the bend.
Experiments indicate approximately, that a right angle bend has radius of 3 times the diameter of the pipe.
Formula for right angle bend:
L_e = 4d/3. Where d is diameter of pipe in inches.
So, L_e = (4 x 12)/3 = 16 feet of straight pipe.

Formula for valves:
L_e = 4d/6.

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 = x² 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
More Pj Problem Strings

What is Time?
St Augustine On Time
Bergson On Time
Heidegger On Time
Kant On Time
Sagay On Time

What is Space?
Newton On Space
Space Governance
Leaders
Imperfect Leaders

Essence Of Mathematics
Toolness Of Mathematics
The Number Line
Variables
Equations
Functions

The Windflower Saga
Who Am I?
Primordial Equilibrium
Primordial Care
Force Of Being
Forgiveness

Blessed are they that have not seen, and yet have believed. John 20:29