FUNDAMENTALS OF WATER ENGINEERING - CVEN9625
Assignment 2 Hydraulics
Individual Assignment Requirements
1.1 Introduction
This assignment covers the Hydraulics component of CVEN9625. You should complete them independently, by having first mastered the CVEN 9625 lecture material as well as having completed the specified Workshop problems. To guide you, the general topic related to each question is identified.
1.2 Assignment Value
The value of this assignment towards your CVEN9625 final course mark is 20%.
1.3 Submission Place, Date and Time
You should submit your solutions to this assignment electronically by uploading it to Moodle. The due date and time are: 11:00 pm (Sydney time) on 27/04/2025. Please note that (i) late assignments (including those submitted after 11:00 pm on the due day) will attract a penalty of 5% per day, capped at five days (120 hours, including weekends), after which the submission will not be accepted. (ii) computer or printer malfunction are not accepted reasons for late submissions. You can submit handwritten solutions, but please ensure that they are legible and easy to read.
1.4 Important Points Relating to the Assignments
Please note:
• You are expected to complete all calculations and setting out yourself - copied assignments (irrespective of whether the assignment was the original or not), may well result in 0 marks being awarded and these assignments will not be returned.
• Submission transmitted electronically, must be contained within a single file. Multiple files of any type containing this assignment will not be accepted,
• The front page of your submission must contain your name, student ID number and your email.
• It is considered that the questions are reasonably straightforward and sometimes a hint is provided to enable you to complete all questions independently. If any well-based queries arise, responses by the Lecturer will be forwarded to the entire class.
1.5 Recommended Nominal Values of Various Parameters
Unless otherwise specified in each question, you may assume the following values:
• p = 1000 kg/m3 = density of fresh water (at 'room' temperature),
• v = 10-6 m2/s = kinematic viscosity of fresh water (at 'room' temperature),
• g = 9.80 m/s2 = acceleration due to gravity,
• Patm = 101.3 kPa = atmospheric pressure, and
• Pvap = 2.3 kPa (abs.) = vapour pressure of fresh water.
Unless stated otherwise, all pressures used in this assignment are relative (also known as gauge) pressures. For example, a relative pressure would be written as (say) 8.5 Pa while an absolute pressure would be written as 8.5 Pa (abs.). It is strongly recommended that you complete all problems using relative pressure.
1.6 Marks
Up to approximately 10% of the total marks for this assignment will be allocated to the clarity of your setting out. Moreover, to encourage you to adopt good problem-solving strategies, you must include one fully annotated diagram for each question, unless otherwise specified.
An indicative allocation of marks has been made to each question, but some changes may be made.
Question 1: Shear Force on a Moving Plate in a Viscous Oil Layer [12 Marks]
A thin 50 cm × 50 cm flat plate is pulled at 3 m/s horizontally through a 3.6-mm-thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 0.3 m/s, as shown in Figure 1. The dynamic viscosity of the oil is 0.027 Pa.s.
Figure 1. A Thin Plate Moving Through a Sandwiched Oil Layer
Assuming the thickness of the plate is negligible, and velocity in each oil layer varies linearly, do the following:
(a) draw the velocity profile and find the location where the oil velocity is zero [5 marks], and
(b) determine the force that needs to be applied on the plate to maintain this motion. [7 marks]
[Hint: The point of zero velocity is somewhere in between the moving plate and moving wall, and its distance from the lower plate can be determined from geometric considerations (the similarity of the two triangles).]
Question 2: Pressure - Manometer [13 marks]
A double column enlarged ends manometer is used to measure a small pressure difference between two points of a system conveying air under pressure, the diameter of U-tube (d) being 1/10 of the diameter of the enlarged ends (D).
The heavy liquid used is water, and the lighter liquid in both limbs is oil with a relative density of 0.82. When p1=p2, the fluids are at the same levels.
Figure 2. Mano meter readings
Assuming the surfaces ofthe lighter liquid to remain in the enlarged ends, determine:
(a) The difference in pressure head(in mm of water) for a manometer displacement of Δ=50 mm. [9 marks]
[Hint: Think about how the volume of fluid displaced in the enlarged ends relates to the U- tube's displacement. What must be true for the volumes to be equal? Understand this can help you find X.]
(b) What would be the manometer reading if carbon tetrachloride (relative density 1.6) were used in place of water, the pressure conditions remaining the same? [4 marks]
Note: You do not need to provide an annotated diagram for this question.
Question 3: Hydroelectric plant Design
This question consists of three tasks related to a hydroelectric plant that discharges water into a large reservoir used to supply water to nearby users, as schematically shown in Figure 3. When data are missing, make your assumptions and state them in your solutions.
Figure 3 Scheme of the plant under study
Task 3.1. Hydrostatics – Forces on plane surfaces [30 Marks]
The artificial reservoir of a hydroelectric plant is obtained via a concrete dam. Water backs up behind the concrete dam, as shown in Figure 3.1a. Leakage under the foundation gives a pressure distribution under the dam as indicated, with pB = γ h and pA = γ hT . If the water depth, h, is too large, the dam will topple over about its toe (point A). The specific weight of the concrete is 25000 N m-3.
Dimensions: L = 11 m, hD = 32 m, hT = 2.5 m, L1= 5 m.
Figure 3.1 Scheme of a concrete dam for Task 1.
Complete the following:
(a) In the case of Figure 3.1a, determine the maximum water depth that can be achieved without dam failure. Conduct your analysis based on one unit length of the dam. [20 Marks]
[Hint: Consider all forces and their locations, then balance the clockwise and counter- clockwise moments about point A to find h.]
(b) If the dam were built with an inclined side upstream (Figure 3.1b), the maximum water depth would change. Calculate the maximum water depth in this second case. [10 Marks]
Task 3.2. Momentum - Thrust against the penstock [18 Marks]
Given the scheme in Figure 3.2, if the diameter of the pipe is 2 m, the angle α is 60˚, the radius of curvature is 6 m, and the flowrate is 35 m3 s-1. Neglect energy losses.
Calculate the thrust of the water against the penstock between the circular sections A and B (provide both magnitude and direction).
Figure 3.2 Scheme of a curving portion of the penstock.
Task 3.3. Pipe flow – Energy losses [27 Marks]
The high-head hydroelectric scheme consists of the reservoir (Figure 3.3) from which the water is delivered to four Pelton turbines through a low-pressure tunnel LT = 10000 m long, 4 m in diameter, lined with concrete. The tunnel splits into four steel pipelines (penstocks) 590 m long, 2 m in diameter each terminating in a single nozzle, the area of which is varied by a spear valve. The maximum diameter of each nozzle is 0.9 m. The difference in level between reservoir and jets is 540 m. Roughness sizes ofthe tunnel and pipelines are 0.1 mm and 0.3 mm respectively.
(i) Find information about the main components of the plant (dam, surge chamber, penstock, spear valve) and briefly (1-2 sentences) describe their role in the plant. [5 marks]
(ii) Determine the effective area of the jets for maximum power (assume the surge chamber to penstock entrance is smoothly rounded, resulting in no energy loss). [10 marks]
[Hint: A commonly used guideline for optimizing hydro systems is that maximum power output is achieved when the total head loss in the system (including friction and local losses) is approximately one-third of the gross head. This balance ensures an optimal trade-off between flow rate and available head, allowing the turbine to operate efficiently while minimizing excessive energy losses. It also aids in determining the ideal nozzle opening for maximum power generation.]
(iii) Determine the difference in level between the water in the surge chamber and in the reservoir under the conditions of maximum power. [4 marks]
(iv) Draw the Energy and the Hydraulic Grade Lines for the system. [8 marks]
Figure 3.3. Scheme of hydraulic plant