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McGill University
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BREE 305
(1)

Vijaya Raghavan
(1)

Lecture

School

McGill University
Department

Bioresource Engineering

Course Code

BREE 305

Professor

Vijaya Raghavan

Description

BERNOULLI VERIFICATION & FLOW PATH FRICTION
LOSSES
BREE 305
FLUID MECHANICS
10/12/2012
-Lab Group 4-
Nada Kahn 260479292
Mark Kim 260426887
Caro Jang 260410441
Raquel Labranche 260480722
Rodger Liu 260399475
Gianni Montanaro 260418092
Chris Panaritis260480361 Introduction:
Bernoullis theorem is the principle of energy conservation for ideal fluids, allowing
engineers to describe, characterize, and model fluid flow allowing for numerous engineering
applications. The theorem states that the total mechanical energy of the flowing fluid, comprising
the energy associated with fluid pressure, the gravitational potential energy of elevation, and the
kinetic energy of fluid motion, remains constant. Additionally, the mathematical expression of
the Bernoulli equation relates pressure, velocity, and elevation in a steady laminar flow to a fixed
constant. However, Bernoullis theorem is limited to the following conditions: flow is steady,
friction is negligible, the fluid holds constant density, and the two points in question lie on the
same stream line.
In this lab, a special apparatus consisting of the flow of water through a tapering circular
duct is designed to verify Bernoullis Theorem. The apparatus mimics the aforementioned
conditions as closely as possible while providing for a way to measure the pressure head via
probe and tapping points. By recording various measurements, and relating them through
equations, we can expect an increase in fluid velocity for converging flow as the fluid moves into
a narrower cross sectional area, and a decrease in fluid velocity for diverging flow as the fluid
moves into a wider cross sectional area. The results of which, will have predictable outcomes on
the total pressure head.
For a practical situation (where Bernoullis conditions are not met) of pumping liquid
from one point to another, it is crucial to account for friction losses in a flow path. Both the size
and length of pipes can be adjusted to compensate for pressure loss/head loss in the pipes due to
frictional forces. Not only does head loss occur in the straight sections of pipe, but also bending
sections of pipe which have additional contributions to pressure head loss. In designing a
functional system involving pipes and liquid, the calculated amount of pressure required is
directly related to the amount of pressure lost due to friction along the pipe. To quantify and
better understand frictional loss through pipes, both the Reynolds number and frictional factor
are calculated.
Primarily, head loss is directly proportional to the amount of friction present and is
described with the friction factor. Using the, Darcy-Weisbach equation it is possible to calculate
the friction factor which is dependent on the both the type of fluid flow and the roughness
coefficient of the pipe. While the roughness coefficient is a constant dependent on the pipe
material, the type of fluid flow is a calculated value called Reynolds number.
To continue, Reynolds number is a dimensionless number that determines the
characteristics of whether a flowing fluid is laminar, transitional or turbulent. If a flow is found
to be laminar, then the friction factor is only dependent on the Re number. When a flow is found
to be turbulent, then the friction factor is dependent on Re number and roughness of the pipe
coefficient of the pipe. Transitional flow is a combination of turbulent and laminar flow, when
2300 < Re < 4000; a state in which the frictional factor cannot be found due to the variation of
flow patterns from turbulent to laminar.
When the head loss is calculated using the Darcy-Weisbach equation, it accounts for the
velocity head, pressure head and elevation head. The velocity head is the pressure felt at a point
placed in front of a flowing fluid. The pressure head corresponds to a height read on a
manometer of a pressure at a point of a fluid at rest. The elevation head is the pressure exerted
from the gravitational forces of the fluid on the pipe.Objectives:
The objective of the first part of the experiment is to use the Bernoullis theorem
verification apparatus to verify water flow, allowing students to test whether the Bernoullis
theorem is being obeyed. The water flow that is being measured flows through a tapering circular
duct that is divided into two sections in a pipe.
The objectives for the second part of the experiment are to determine the friction loss
of water flow through a circular pipe and to observe and discussing the resulting graph of friction
factor vs. the Reynolds number. Another objective of this experiment is to estimate and observe
the head loss coefficient in the bend of the circular pipe.
Materials & Methods:
Materials 2.1 & 2.2
Hydraulic bench F1-10
Bernoulli's Theorem demonstration apparatus F1-15
Stopwatch
Buckets
Weigh scale
Procedure 2.1 - Bernoullis Theorem Verification Apparatus
1. The apparatus was leveled on the hydraulic bench using the adjustable feet.
2. The apparatus nanometer tubes were filled w

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