BREE 305 Lecture Notes - Reynolds Number, Fluid Mechanics, Dimensionless Quantity

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Published on 21 Nov 2012
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BREE 305
-Lab Group 4-
Nada Kahn 260479292
Mark Kim 260426887
Caro Jang 260410441
Raquel Labranche 260480722
Rodger Liu 260399475
Gianni Montanaro 260418092
Chris Panaritis 260480361
Bernoulli’s 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, Bernoulli’s 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 Bernoulli’s 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 Bernoulli’s 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.
The objective of the first part of the experiment is to use the Bernoulli’s theorem
verification apparatus to verify water flow, allowing students to test whether the Bernoulli’s
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
Weigh scale
Procedure 2.1 - Bernoulli’s Theorem Verification Apparatus
1. The apparatus was leveled on the hydraulic bench using the adjustable feet.
2. The apparatus nanometer tubes were filled with water to discharge all pockets of air from the
system. it was ensured that all connecting pipes were free from air.
3. The inlet feed and the flow control valves were carefully adjusted to provide the combination
of flow rate and system pressure, which would result in the largest convenient difference
between highest and lowest nanometer levels.
4. The probe was inserted to tapping No.1 and then moved into the tapped portion, starting at
5. The final reading was taken at No.6 and the distance from the end of the parallel portion and
scale readings of its manometer level were noted and recorded for each position.
6. The inlet feed was stopped, the apparatus drained off, the full length of the probe was
withdrawn, the couplings were undone, the test sections were reversed and the couplings were
then replaced.
7. Steps 1-5 were repeated.
Procedure 2.2 - Friction Losses in a Flow Path
1. The inner diameter of the pipe was measured and the length of the pipe between the two points
of pressure measurement was determined.