Hydrostatic and Hydrodynamic Problems in Civil Engineering Hydraulics

This assignment solution addresses various hydraulic engineering problems. Task 1 calculates pressure in a pipe and compares it to open channel pressure, discussing factors affecting water flow like viscosity, boundary layers, and flow regimes (laminar vs. turbulent). Task 2 applies the Gauckler-Manning formula and Darcy-Weisbach equation to determine flow rate, depth, and velocity in open channels and pipes. Task 3 delves further into pipe flow, calculating head losses, fluid velocity, and pipe diameter, while considering factors for choosing between open channel and pipe systems, including cost, safety, and fluid type. Finally, Task 4 addresses hydrostatic pressure on a car park floor and recommends materials for construction. The solution incorporates relevant formulas and concepts from fluid mechanics and hydraulics, providing a comprehensive analysis of the given scenarios.

Hydraulics for Civil Engineering 1
HYDROSTATIC AND HYDRODYNAMIC PROBLEMS
By Name
Course
Instructor
Institution
Location
Date

Hydraulics for Civil Engineering 2
TASK 1
Height above the city = Height = 100 m
Water Density = 1000 kg/m3
Gravitational pull = 9.8N/Kg
Pressure in pipe, P = 100 x 1000 x 10 N/m3
Pressure in pipe = 1,000,000N/m2
When converted into Bar: Pressure in Pipe = 10 Bar
(Diamantis, Papageorgiou, & Kosmatopoulos, 2010)
Since in open channel system the water flow due to the effects of atmospheric pressure, the
pressure bringing water into the city center is equal to the atmospheric pressure:
Therefore:
Atmospheric Pressure, PAtmo = Open Channel Pressure
PAtmo = 100,000 N/m2
Open Channel Pressure = 100,000N/m2
The pressure in pipe system is 1,000,000N/m2 while open channel pressure is 100,000N/m2,
this means that the pipe system pressure is higher compared to open channel pressure since in
pipe channel system may be flowing as a result of external pressure such as pumping action
(Bing & Yang, 2011).
The major forces of resistance to flow of water in pipes include boundary layer effect and
frictional force in water (viscosity). The effects of boundary layer is a resistive force that is
caused by sticking of fluid on the solid bordering it. This sticking effect in the boundary layer
reduces the velocity of fluid flow gradually and the fluid near the boundary do not flow at all.

Hydraulics for Civil Engineering 3
Viscosity of the frictional force in fluids and is caused by internal friction between the fluid
molecules themselves or between the fluid molecules and the surface of the container (Ercan &
Kavvas, 2013).
An increase in temperature may either increase or decrease the viscosity or the boundary layer
effect depending on the physical state of the water. An increase in temperature decreases the
viscosity effect on the flowing fluid since an increase in temperature decreases the cohesion
forces and increasing kinetic energies of the molecules hence reducing the viscosity of fluid. A
decrease in temperature affect the viscosity of fluid since the decrease in temperature
increases the cohesion forces and decreases the kinetic energies of the molecules hence
increasing the viscosity of the fluid.
The increase in temperature decreases the boundary layer effect of the fluid by increasing the
kinetic energies of the flowing fluid hence mobility of molecules is also increased. A decrease
in temperature increases the boundary effect of the fluid by decreasing the kinetic energies of
the flowing fluid hence mobility of molecules is also decreased (Zimmermann, 2010).
Laminar flow which is also referred to as streamline flow and occurs when fluid flows in
parallel layers without any disruptions between the fluid layers. At low velocities, there is a
tendency of the fluid to flow without mixing laterally. There are no swirls, eddies, or cross-
currents perpendicular to the flow direction (Friedrich & Stemmer, 2014).
Turbulent flow is a disorderly or chaotic flow resulting into variations in flow velocity and
pressure in time and space. The fluid does not flow in in layers as in the case of laminar flow.
The flows at Reynolds number greater than 4000 are generally turbulent (Widodo & Pradhana,
2018).
The Reynolds number is fluid mechanic quantity used for the flow pattern prediction in
various fluid flow conditions. At low Reynolds number below 2300, the fluid flows is laminar
characterized by smooth and orderly flow while at high Reynolds number higher than 2300,
the fluid flow tend to be turbulent flow characterized by disorderly flow (Chamorro & Arndt,
2011).

Hydraulics for Civil Engineering 4
A boundary layer is a relatively thin layer of fluid close to the surface of the body neighboring
the fluid flow. The boundary layer tend to affect the flow of fluid by having a pull effect of the
flowing hence reducing the fluid velocity especially near the borders between the fluid and the
soil surface.
The physical state of the surface over which water is flowing influences the boundary layer
since a very smooth surface results in laminar flow of fluid over the surface since there are no
disturbances hence increasing the boundary layer. In case the surface in which water is
flowing over is rough, then there will be disorderly or turbulence which reduced the boundary
layer between fluid and the surface.
Some of the ways in which the resistance of water flow can be reduced in open channel system
or pipe system include:
Reducing water flow velocity: High velocity of water flow causes turbulence hence resulting
into resistance to the flow of water. By reducing the velocity, the flow of water will be smooth
without any resistance (Ghosh, Friedrich, & Stemmer, 2014).
Increasing the temperature of water flowing in the pipe: By increasing the temperature of the
flowing fluid, the viscosity will be reduced hence no resistance between water molecules or
between water molecules and the pipe surface.
Reducing the length of pipe: The longer the pipe, the higher the resistance between the fluid
molecules themselves and also between the fluid molecules and the surface of open channel or
pipe. Therefore, the resistance of water flow is reduced by reducing the length of the flow
channel.
Increasing the pipe diameter: The diameter of the pipe affects the velocity of water flowing
through the pipe. The larger the pipe diameter the lower the resistance of water flow (Garai,
Pardyjak, & Steeneveld, 2013).

Hydraulics for Civil Engineering 5
By letting the water supply pressure from the source = P initial
The initial water pressure reaching the residences = P Residences
New pressure after additional supplies = P New
Pressure of additional supplies, P Addition
Initially, water supplied from the source was enough for the residences, therefore:
P initial = P residences.
By increasing the number of residences, the pressure of water supplied from the source shall
be lower than the required pressure; P initial ¿P New.
To prevent disruption of the current supplies, the additional supplies can be piped by adding
the pressure of the additional supplies to the initial pressure.
Therefore, the new supplied pressure; P New = P Addition + P initial
(Holzner, Song, & Avila, 2013)

Hydraulics for Civil Engineering 6
TASK 2
By applying Gauckler-Manning formula for this open channel system:
Flow Rate, Q = [ 1.49
n ] x A x { Rh
2 /3 } S1 /2
Gauckler-Manning Coefficient = 0.02 = n
Flow Rate = 30m2/s = Q
Cross-sectional Area = 2m = y [ Assuming thecanal system isrecatngular ∈shape ]
The Rectangular Base Width = 2 m = b
For a Normal water flow in a canal system,
Fluid Velocity = 1
2 R [ h2/ 3 ] [ S1 /2 ] = V
Area, A = Base width x Depth of Flow ¿ bh
Substituting the A = bh in the equation, Rh = bh
b+2 h
h= h
1+2 h/b , Replacingb=2
2 h= h
1+2 h/2 ; 2 h ( 1+h )=h
h=0.5
The Flow Depth = 0.5 m
(Lopez & Walters, 2015)

Hydraulics for Civil Engineering 7
Darcy Friction Factor = 0.006 = f
Volumetric Flow Rate = 10m3/s = Q
Pipe Length = 2000 meters = L
Diameter of Pipe = 1.5 meters = D
Earth’s Gravitational Pull = 10 N/kg = g
Fluid Flow Velocity =
Volumetric Flow Rate
Area of Pipe = 10 m3 / s
22
7 x 0.75 x 0.75
=5.7 m/s
By making these substitutions in the Darcy-Welsbach Equation:
hL=L x ( V 2
D )x ( 1
2 g ) x f
Substituting the values above to the formula:
hL=2000 m x ((5.7 m/s )2
1.5 m )x ( 1
2 x 10 N /kg ) x 0.006
hL=12.8 meters
(Ciprian, 2019)

Hydraulics for Civil Engineering 8
Pressure developed due to Height difference, P = Height difference x Density of water x
Gravity
Pressure developed by water fall=50 x 1000 x10 = 500,000 N/m2
For Flow Rate of 30m3/s to be achieved, then the pressure due to this flow rate should be less
than the pressure developed du rot height difference
Therefore due to 30m3/s Flow Rate¿ 1
2 (V 2
2 +V 1
2
) x ρ; Where V2 = 0 m3/s and V1 = 10 m3/s
Pressure = 1
2 x 102 x 1000 kg /m3 = 50,000N/m2
Since the pressure developed as a result of height difference is greater compared to the
pressure required to deliver the flow rate of 30m3/s, then it is possible to achieve the flow rate
required. The step that should be taken is to channel the water dropping through the height to
a pipe so that water can flow through it at the required flow rate (Donskov & Donskov, 2013).

Hydraulics for Civil Engineering 9
In pipe flow, the fluid flow is as a result of hydraulic pressure while in open channel flow, the
flow is as a result of atmospheric pressure. In pipe flow, the area of flow is fixed dimensions
of the pipe, while in open channel, the area of flow is affected by the surface level and
geometry of the open channel.
Dimensions of Open Channel
Since Flow Rate = 10m3/s = Q
Normal Depth = 2meters = y
By assuming that the open channel is Rectangular in shape:
Replacing the Normal depth, y = 2m to determine Area, Perimeter, and Hydraulic Radius of
the open channel:
Channel Width, B = 2y = 4 m
Channel perimeter, P = 4 x Length = 4 x y = 4 x 2 = 8 m
Cross-section Area, A = By; But B = 2y
Therefore, Area, A = 22 x 2 = 8m2
Hydraulic Radius = = y
2 =2 m
2 =1.0 meters=Rh
V, Fluid Flow Velocity = Area
Flow Rate = 8 m2
103 / s = 0.8m/s
(Roushangar, Mirza, & Mouaze, 2012)

Hydraulics for Civil Engineering 10
TASK 3
From the Darcy-Welsbach Equation:
hL=L x ( V 2
D ) x ( 1
2 g ) x f
Q = Flow Rate = 30 m3/s
L = Length of Pipe = 10,000 m
F = Darcy Friction Factor = 0.004
D = Diameter of the Pipe =1.4 m
V = Fluid Flow Velocity = ?
Fluid Flow Velocity Flow Rate
Area of Pipe =¿
30
22
7 x 0.7 x 0.7
=19.5 m/s
Substituting the parameters above:
hL=10,000 x ( 19.52
1.4 ) x ( 1
20 ) x 0.004
Head Loss , hL=543.2meters
Minor losses = 10 x 19.5 = 195m
The Total Head Losses = (195 + 543.2) meters
= 738.2 meters
(Liakopoulos, Sofos, & Karakasidis, 2017)

Hydraulics for Civil Engineering 11
The difference in Height, Height = 20 meters
Water Density = 1000kg/m3
Extra Pressure Required = Pressure due to water column
= hρg=20x1000x10 = 200,000N/m2
Extra Pressure to be supplied by a pump = 200,000N/m2
By applying Fluid Flow Velocity:
Difference in Pressure = 1
2 (V initial
2 +V final
2
) x ρ
Difference in Pressure = 1
2 x ( V initial
2
) x 1000=200,000
( V initial
2
)= 200,000
400
Fluid Flow Velocity = 20m/s
The Smallest Diameter of Pipe:
Cross Sectional Area of Pipe = Flow Rate
Fluid Flow Velocity =30 m3 /s
20 m/s =1.5 m2
Area = ΠR2 = 1.5 m2
Radius, R2 = 1.5
Π =0.477
R = 0.691m
Therefore, Smallest Diameter, D = 1.382 meters
(Widodo & Pradhana, 2018)

Hydraulics for Civil Engineering 12
Factors to consider when deciding the flow channel to use
Cost
Open channel is the cheapest channel of transporting fluid since the flow is as a result of
atmospheric gravity while pipe system entail the use of pumping mechanism and also pipes
which have to be purchased.
Safety
Pipe based system is safer compared to the open channel based system since the fluid is
enclosed in the pipe without any exposure. However, in open channels, the fluid can be
accessed since the fluid flowing can easily accessed by unauthorized person.
Type of Fluid
Fluids like gases can only be transported through pipe system. Volatile fluids need to be
enclosed during transportation.
Pressure Required
In case there is need of pressure in the fluid to be transported, then pipe system is suitable
since it is easy to regulate pressure through pumping action.
(Jamshidnia, Tasaka, & Murai, 2010)