Hydraulics 3A Semester Test 1 1
PROGRAM : BACCALAUREUS INGENERIAE
CIVIL ENGINEERING SCIENCE
SUBJECT : Hydraulics Engineering 3A
CODE : HMG3A
Instructor : Dr S Rwanga
Type : Semester Test 1
Date : 19 March 2024
Duration : 2.5 hours
TOTAL MARKS : 70
INSTRUCTIONS TO STUDENTS
• CLOSED BOOK
• PLEASE ANSWER ALL QUESTIONS
• PROVIDE PRECISE ANSWERS FOR THE THEORETICAL PART
• SHOW ALL THE STEPS FOR THE CALCULATION PART
• RETURN QUESTION PAPER
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QUESTION 1 [20]
1.1 Describe the concept of hydraulic grade line (HGL) and its importance in hydraulic design (4)
“The hydraulic grade line (HGL) represents the sum of the pressure head and elevation head in a fluid flow
system. It is an essential concept in hydraulic design, as it helps engineers visualize the energy distribution
along a pipeline or channel and identify potential issues related to pressure fluctuations and flow velocities.
The importance of HGL lies in its ability to guide engineers in designing efficient and safe hydraulic systems.
For instance, by analyzing the HGL profile, engineers can determine if there are any locations where excessive
pressure might cause pipe failure or if there’s insufficient pressure for proper functioning. Additionally,
understanding the HGL allows engineers to optimize pump selection and placement, ensuring that the system
operates within acceptable limits while minimizing energy consumption. In summary, the HGL serves as a
valuable tool for evaluating and optimizing hydraulic designs, ultimately contributing to the overall
performance and safety of fluid flow systems.”
1.2 The two reservoirs illustrated are used for water storage and supply. The water levels in the reservoirs are
constant and equal to 70 m AOD in the lower reservoir (Reservoir A) and 82 m AOD in the upper reservoir
(Reservoir B). The reservoirs are connected by a 1.2 km long pipe with diameter 𝐷 = 200 mm and wall
roughness 𝑘𝑠 = 2×10−4 m, 𝜈 =1.0×10−6 m2 s−1 . A pump is installed in the pipe as illustrated in the figure 1.
Neglecting minor losses,
i. Sketch the qualitative behaviour of the energy and hydraulic grade lines between Reservoir A and
Reservoir B if the system operates under gravity alone (i.e. without the pump). (3)
ii. Sketch the qualitative behaviour of the energy and hydraulic grade lines between Reservoir A and Reservoir
B when the pump is operating, and the flow direction is from Reservoir A to Reservoir B; (3)
Instructor: Dr S Rwanga 19/03/2024
Hydraulics 3A Semester Test 1 3
iii. Find the pump head required to deliver a discharge of 0.025 m3/sec to reservoir B. Use Colebrook-White
equation to calculate for f, assume initial f = 0.01. Perform one iteration only for f value. (10)
Figure 1
SOLUTION
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QUESTION 2 [16]
Water is to be discharged from a reservoir at a rate of 18 L/sec using two horizontal carbon steel pipes connected
in series with a pump between them as shown in Figure 2. The first pipe is 20 m long and has a 6 cm diameter,
while the second pipe is 35 m long and has a diameter of 4cm. The water level in the reservoir is 30 m above
the centreline of the pipe. The pipe entrance is sharp-edged (K =0.5), and losses associated with the connection
to the pump are negligible. Determine the minimum pumping power required to maintain the indicated flow
rate. Use Barr equation while solving for f. Use kinematic viscosity of 1 x 10-6 m2/sec.
Figure 2
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SOLUTION
By using white Colebrook – The calculation are based on this approach
However, using Barr equation yield =14.200 m.
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QUESTION 3 [18]
Calculate the pipe diameter using Type 3 approach. Given the following information.
Pipe length = 10 km
Flow rate =700 l/sec
Density of water is 1000 kg/m3.
Dynamic viscosity is 1.307 x 10-3 kg.ms
Friction head loss (hf) = 42 m
Absolute roughness 0 0.3 mm
For first iteration use f = 0.02.
Use Jain equation for further iterations.
Calculate three iterations only.
Show all steps.
REFER SOLUTION FROM CLASS NOTES
QUESTION 4 [26]
Figure 3 shows a water distribution network with one inflow node at point A and three outflow nodes at B, D
and E. Table 1 presents the elevation of all nodes. Table 2 presents pipe characteristics, diameter, and length.
Assume water T = 20 o C. Use dynamic viscosity of 0.0010005 Ns/m2
Instructor: Dr S Rwanga 19/03/2024
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Figure 3
i. Determine the value of QE (2)
ii. Determine the flows (after 2 iterations) in the pipes using Darcy-Weisbach Method (16)
[Hint: Assume Q for pipe AB = 120 L/s for initial trial
iii. Determine the pressure heads at each node if the pressure head at reservoir X is 60 m. (6)
Note: Use appendix 1 for water network calculations. Show sample calculation for one pipe only.
Table 1: Elevation nodes Table 2: Pipe characteristics
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SOLUTION DEPENDS ON INDIVIDUALS
STUDENT NUMBER: STUDENT NAME: Appendix 1
Pipe Qo D L Re f Qc
Pipe Qo D L Re f Qc
Iteration =
Pipe Qo D L Re f Qc
Pipe Qo D L Re f Qc
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IMPORTANT FORMULA SHEET
ℎ𝑜𝑟𝑖𝑧 =
(∆𝑃−𝜌𝑔𝐿𝑠𝑖𝑛𝜃)𝜋𝐷 4
128𝜇𝐿
𝜌𝑉𝑎𝑣𝑔 𝐷
𝑅𝑒 =
𝜇
hf 2g 5
Q= D
L 8f
Q = AV V2
hs = K
2g
Ku 2 / 3 1 / 2
V = R So
n
Note : λ is f
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Instructor: Dr S Rwanga 19/03/2024
