Hydraulics for Civil Engineering - Fluid Mechanics Analysis

This document presents a comprehensive hydraulics assignment solution for civil engineering students, covering key concepts in fluid mechanics. The assignment delves into the calculation of water pressure from a reservoir, differentiating between open channel and pipe flow, and analyzing the impact of viscosity and temperature on water flow. It explores the significance of the Reynolds number and boundary layers. The solution includes detailed calculations using the Manning and Darcy-Weisbach equations to determine flow rates, head loss, and pressure requirements in both open channels and pipe systems. The document also addresses practical considerations such as material selection for car park walls and the comparison of open channel and pipe systems based on factors like cost, safety, and pressure regulation. References to relevant research papers are also provided.

Hydraulics for Civil Engineering 1
UNIT 43 HYDRAULICS
By Name
Course
Instructor
Institution
Location
Date

Hydraulics for Civil Engineering 2
TASK 1
Water Pressure from Reservoir = H x ρ x g
= 100 x 1000 x 10
= 1,000,000 N/m2 OR 10 bar
In an open channel, the pressure is 0 Bar since the flow is as a result of only gravitational
force and the flow boundary can easily be deformable hence shear stress and pressure are
zero1.
Boundary layer: The layer of fluid is the immediate vicinity of the surface bounding where the
impacts of viscosity are substantial affects the water flow in the pipes
Viscosity: This is the drag force that occurs between the layers of water in the pipes or
between water and the walls of the pipe hence affecting the flow of water in the pipe2.
An increase in temperature affects the viscosity of water by decreasing the density of the liquid
and lower density reduces the viscosity of water. Reduced density caused by an increase in
temperature also weakens the boundary layer. By reducing the temperature of water, the
viscosity and boundary layer are increased up to specific temperature before water freezes into
ice.
1 Ercan, A. & Kavvas, L., 2013. Scaling and self-similarity in one-dimensional unsteady open channel flow.
Hydrological Processes, Volume 28, pp. 2721-2737.
2 Zimmermann, A., 2010. Flow resistance in steep streams: An experimental study. Water Resources Research,
Volume 46.

Hydraulics for Civil Engineering 3
This is a value that is dimensionless which determines the ratio of inertia forces to viscous
forces and illustrates the turbulent or laminar flow degree3.
The boundary layer is the water layer in the direct contact of the surface bounding where the
impacts of viscosity are noticeable. The roughness of the surface over which water is flowing
promotes the transition to turbulence in the boundary layer hence resulting into early
separation caused by increased momentum and drag deficit.
Water flow resistance in open channel or pipe can be reduced by: Increasing temperature of water in open channel or pipe
 Decreasing the flow velocity of water in open channel
 Decreasing the length of the pipe
 Increasing the pipe diameter4
By subsequently increasing the pressure of water from the distribution point, the additional
supplies will be accommodated within the supply and the current supplies will not be affected.
The pressure of water in each household in the current supplies should be determined first so
that the value will be used to increase the pressure of distribution depending on the number of
additional supplies5.
TASK 2
3 Glazner, A., 2014. Magmatic life at low Reynolds number. Geology, Volume 42, pp. 935-938.
4 Diamantis, M., Papageorgiou, M. & Kosmatopoulos, E., 2010. Identification and Adaptive Control for Open
Channel Water Flow Systems. Computer-Aided Civil and Infrastructure Engineering, Volume 26, pp. 464-480.
5 Bing, H. & Yang, L., 2011. Flow Velocity Coefficient Research on the Coexistence of Pipe Flow and Flow around
Pipe. Advanced Materials Research, Volume 204, pp. 746-749.

Hydraulics for Civil Engineering 4
Given that:
Flow rate, Q = 30m3/s
Manning Roughness coefficient, n = 0.02
For the given rectangular channel: A = byo = 2yo
Bottom slope = S
Depth of flow = yo
Manning Equation is given by: Q = (1.49/n) A (Rh 2/3)S1/2
P = b + 2yo = 2 + 2yo and Rh = A/P = 2yo / 2 + 2yo
By rearranging the equation;
Qn
1.49(S1/ 2) = ( Rh
2
3 )
(30 x 0.02
1.49 x S
1
2
)= {2 yo } [ 2 y o
2 +2 yo ]2/ 3
0.6
1.49 = { 2 yo } [ 2 y o
2 +2 yo ]
2/ 3
0.4026= { 2 y o } [ 2 yo
2 + 2 yo ] 2/ 3
yo =0.20
OR 0.2555=[ 2 yo
2 +2 yo ]
yo =0.296
Therefore, Depth of Flow, yo =0.2 m∨0.296 m
6
6 Vatankhah, A., 2012. Direct Integration of Manning-Based GVF Equation in Trapezoidal Channels. Journal of
Hydrologic Engineering, Volume 17, pp. 455-462.

Hydraulics for Civil Engineering 5
Given that:
Diameter, D = 1.5m
Length of pipe, L = 2000m
Moody friction factor, f = 0.006
Flow rate, Q = 10m3/s
Average Velocity, V = Q
A = Q
Π D2
4
= 10
Π 1.52
4
¿ 10
1.7679
¿ 5.656
Darcy Weisbach Equation; hL
L =f ( 1
2 g ) ( V 2
D )
hL=f ( 1
2 g ) ( V 2
D ) x L
hL=0.006 x 1
2 x 10 x 14.142
1.5 x 2000
hL=12.8 m
7
7 Ciprian, B., 2019. The Quest for the Ideal Darcy-Weisbach Friction Factor Equation from the Perspective of a
Building Services Engineer. Ovidius University Annals of Constanta - Series Civil Engineering, Volume 21, pp. 65-73

Hydraulics for Civil Engineering 6
The pressure from the river = H x ρ x g
= 50 x 1000 x 10
= 500,000 N/m2 OR 5 bar
Pressure of Water to reservoir = 1
2 ρ(V 2
2 +V 1
2 )
1
2 x 1000(102+252)
¿ 362,500 N /m2∨3.62¯¿
Yes, it is possible.
This means that the pressure from the river is sufficient to attain the 10m3/s flow rate since the
pressure from the river can supply the required pressure to open the valve when the flow rate
of 10m3/s is achieved8.
In pipe flow, the flow generally occur as a result of pressure difference while in open channel
flow, the flow occurs as a result of gravity9.
Dimensions of the open channel:
Water velocity, V = 1.25m/s
Area, A = 0.5 x (2+6) x 2 = 8m2
Wetted Perimeter, P = 2 √22 +22+ 2 = 7.657
Hydraulic Radius, Rh = A
P = 8
7.657 =1.0448
Flow Rate, Q = VA = 10m3/s
8 Widodo, E. & Pradhana, R., 2018. Analysis of pipe diameter variation in axial pumps for reducing head loss. IOP Conference
Series: Materials Science and Engineering, Volume 403, p. 120.
9 Donskov, G., P, L. & Donskov, D., 2013. Shortcomings of the Darcy-Weisbach equation in blast-furnace smelting. Steel in
Translation, Volume 43, pp. 197-202.

Hydraulics for Civil Engineering 7
TASK 3
Given that;
Flow Rate, Q = 30m3/s
Pipe Diameter, D = 1.4m
Length of pipe, L = 10,000m
Moody friction factor, f = 0.004
Water velocity, V =
Q
A = Q
Π D2
4
30
Π 1.42
4
=19.45 m/s
Minor losses = 10 x velocity head = 10x 19.45 = 195.5m
Darcy Weisbach Equation is given by:
hL
L =f ( 1
2 g ) ( V 2
D )
hL=f ( 1
2 g ) ( V 2
D ) x L
hL=0.004 x ( 1
2 x 10 ) ( 19.452
1.4 )x 10,000
hL=540.43 m
Head loss = 192.5 + 540.43
= 735.93m
10
10 Roushangar, K., Mirza, S. & Mouaze, D., 2018. Linear and non-linear approaches to predict the Darcy-Weisbach
friction factor of overland flow using the extreme learning machine approach. International Journal of Sediment
Research, Volume 33, pp. 415-432.

Hydraulics for Civil Engineering 8
Additional Pressure Required, P = H x ρ x g
= 20 x 1000 x 10
= 200,000 N/m2 OR 2 bar
Pipe Diameter can be determined by;
Area of Pipe, A = Q, Flow Rate
V , Velocity
Q
V ¿ Π D2
4
D2= 4 Q
ΠV
D= √ 4 Q
ΠV
Safety: For the case of those fluids such as oil which are dangerous or explosive and should be
transported through enclosed pipes, then open based channels are not considered as options in
such cases.
Cost: Gravity based system is generally cheaper than pipe based system since the movement of
fluids is through gravity and may not require pumping or use of pipes during operation. Pipe
based system is costly since in most cases pumping action is involved so as to create the pressure
difference and also pipes must be laid down11.
Need for pressure and velocity regulation: In case there is need of regulating the pressure of
water such as for domestic purposes, then pipe based system is generally most applied since it is
11 Widodo, E. & Pradhana, R., 2018. Analysis of pipe diameter variation in axial pumps for reducing head loss. IOP
Conference Series: Materials Science and Engineering, Volume 403, p. 120

Hydraulics for Civil Engineering 9
easier to regulate the velocity and pressure of water through pumping action. In gravity system,
the pressure and velocity cannot be regulated since the flow is majorly based on gravity alone.
Hygiene purposes: When it comes to sensitive fluids such as water for consumption, there is
need of ensuring that water is not exposed to the environment where contamination is most likely
to occur. Pipe based system is hygienically safe for transporting water to be used for human
consumption compared to gravity based system where water is openly exposed to the
environment where pollution is rampant.

Hydraulics for Civil Engineering 10
TASK 4
Pressure Exerted on the Boundary Walls by Water = H x ρ x g
= 1.5 x 1000 x 10
= 15,000 N/m2
Car Park Area on Boundary Wall, A = 20 x 60 = 1,200m2
Pressure, P = Force , F
Area , A
Force on Boundary Wall, F = Pressure x Area
F = 15,000 x 1,200 = 18,000kN
Precast concrete materials is the most recommended material that can be used in the
construction of outer walls of the car park so as to act as the major structural support for the
building. The major reason for selecting precast concrete is due to the durability and strength
of the material.
Precast concrete is also the best material that can be used for flooring because of its durability
and structural strength and then performing final finish with resin coating to provide
moisture proofing which is very common in basements12.
12 Bing, H. & Yang, L., 2011. Flow Velocity Coefficient Research on the Coexistence of Pipe Flow and Flow around
Pipe. Advanced Materials Research, Volume 204, pp. 746-749.

Hydraulics for Civil Engineering 11
REFERENCES
Bing, H. & Yang, L., 2011. Flow Velocity Coefficient Research on the Coexistence of Pipe Flow and Flow
around Pipe. Advanced Materials Research, Volume 204, pp. 746-749.
Ciprian, B., 2019. The Quest for the Ideal Darcy-Weisbach Friction Factor Equation from the Perspective
of a Building Services Engineer. Ovidius University Annals of Constanta - Series Civil Engineering, Volume
21, pp. 65-73.
Diamantis, M., Papageorgiou, M. & Kosmatopoulos, E., 2010. Identification and Adaptive Control for
Open Channel Water Flow Systems. Computer-Aided Civil and Infrastructure Engineering, Volume 26, pp.
464-480.
Donskov, G., P, L. & Donskov, D., 2013. Shortcomings of the Darcy-Weisbach equation in blast-furnace
smelting. Steel in Translation, Volume 43, pp. 197-202.
Ercan, A. & Kavvas, L., 2013. Scaling and self-similarity in one-dimensional unsteady open channel flow.
Hydrological Processes, Volume 28, pp. 2721-2737.
Glazner, A., 2014. Magmatic life at low Reynolds number. Geology, Volume 42, pp. 935-938.
Roushangar, K., Mirza, S. & Mouaze, D., 2018. Linear and non-linear approaches to predict the Darcy-
Weisbach friction factor of overland flow using the extreme learning machine approach. International
Journal of Sediment Research, Volume 33, pp. 415-432.
Vatankhah, A., 2012. Direct Integration of Manning-Based GVF Equation in Trapezoidal Channels.
Journal of Hydrologic Engineering, Volume 17, pp. 455-462.
Widodo, E. & Pradhana, R., 2018. Analysis of pipe diameter variation in axial pumps for reducing head
loss. IOP Conference Series: Materials Science and Engineering, Volume 403, p. 120.
Zimmermann, A., 2010. Flow resistance in steep streams: An experimental study. Water Resources
Research, Volume 46.