A rectangular channel with width B1 [m] has a smooth and gradual contraction B2 [m] in...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A rectangular channel with width B1 [m] has a smooth and gradual contraction B2 [m] in the direction of flow. Downstream of the contraction, the channel width remains constant B3 [m] with identical width as in the contraction B2 [m]. The channel width B1 is provided in your data set, but the widths B2 B3 are unknown. The constant flow rate Q [1/s] is also provided as well as the upstream flow depth y1 [m] which is given when the flow depth at position 1 is not affected by choking flow. At position 2 the channel has in addition to the channel contraction, a hump with height Az [m] which is provided in your data set. Downstream of the hump, the flow enters a long channel with slope S and surface roughness ks. Both channel slope and surface roughness are given in your data set. At a position 3, some length downstream of the hump. the channel will achieve uniform flow conditions. While the surface roughness must be taken into account for the long reach downstream of the contraction/hump, any friction losses between sections 1 and 2 can be assumed small and potential local losses can be neglected. Figure 1 illustrates the setup in both plan and side view; the flow is from left to right. B1 [m]: 1.9 Delta_z [m]: 0.07 Q [L/s]: 480 y1 [m]: 1.19 Slope []: 0.0018 Roughness ks [mm]: 1.43 To find : 1) Find the minimum contraction width B2.c [m] for which the upstream water level is not affected. 2) Calculate the upstream flow depth y1 (or yl' in case of flow choking) and the flow depth in the transition y2 for two cases of contraction width: i)B2 =0.5xB2,c 11)B2 =2xB2.c 3) Sketch one specific energy diagram for three flow scenarios comprising the critical flow case for B2.c (Part 1), and the two flow conditions from Part 2 (Part 2i & ii). For these three scenarios indicate all relevant quantities on your specific energy sketch (e.g. locations of your upstream flow depth y1 (or y1'), your flow depth in your contraction y2, your critical flow depths y1.c and y2.c, the hump height Az, the specific energy in sections 1 and 2, etc.). Marks will be given for clarity and completeness of your sketch. Use colour to improve the readability of your sketch if required. All three scenarios must be sketched in one specific energy diagram and marks will be deducted should you provide three diagrams. (Note: a sketch means that you do not need to draw to scale.) 4) For the critical flow case for B2,c (Part 1), calculate the normal flow depth y3 at a distance downstream of your hump (position 3). The channel is long enough to achieve uniform flow conditions. What is the Froude number at position 3? 5) For the critical flow case for B2,c (Part 1), classify your free-surface profile [gradually varied, rapidly varied and uniform flow] and sketch your free-surface profile along the channel, including all the relevant features. Indicate the different flow regimes (i.e. supercritical, critical or subcritical flow) along the channel. 6) State and explain two of the assumptions involved in writing the following equation: v12 v22 z1+y1 + 2g = z2 + y2 + 2g Where z is the elevation of the channel bed, y is the water depth, v the average flow velocity and g is the gravity acceleration; the subscripts 1 and 2 represent the respective points in the channel. Please note that, if you address more than two assumptions, only the first two will be considered for marking purposes. A rectangular channel with width B1 [m] has a smooth and gradual contraction B2 [m] in the direction of flow. Downstream of the contraction, the channel width remains constant B3 [m] with identical width as in the contraction B2 [m]. The channel width B1 is provided in your data set, but the widths B2 B3 are unknown. The constant flow rate Q [1/s] is also provided as well as the upstream flow depth y1 [m] which is given when the flow depth at position 1 is not affected by choking flow. At position 2 the channel has in addition to the channel contraction, a hump with height Az [m] which is provided in your data set. Downstream of the hump, the flow enters a long channel with slope S and surface roughness ks. Both channel slope and surface roughness are given in your data set. At a position 3, some length downstream of the hump. the channel will achieve uniform flow conditions. While the surface roughness must be taken into account for the long reach downstream of the contraction/hump, any friction losses between sections 1 and 2 can be assumed small and potential local losses can be neglected. Figure 1 illustrates the setup in both plan and side view; the flow is from left to right. B1 [m]: 1.9 Delta_z [m]: 0.07 Q [L/s]: 480 y1 [m]: 1.19 Slope []: 0.0018 Roughness ks [mm]: 1.43 To find : 1) Find the minimum contraction width B2.c [m] for which the upstream water level is not affected. 2) Calculate the upstream flow depth y1 (or yl' in case of flow choking) and the flow depth in the transition y2 for two cases of contraction width: i)B2 =0.5xB2,c 11)B2 =2xB2.c 3) Sketch one specific energy diagram for three flow scenarios comprising the critical flow case for B2.c (Part 1), and the two flow conditions from Part 2 (Part 2i & ii). For these three scenarios indicate all relevant quantities on your specific energy sketch (e.g. locations of your upstream flow depth y1 (or y1'), your flow depth in your contraction y2, your critical flow depths y1.c and y2.c, the hump height Az, the specific energy in sections 1 and 2, etc.). Marks will be given for clarity and completeness of your sketch. Use colour to improve the readability of your sketch if required. All three scenarios must be sketched in one specific energy diagram and marks will be deducted should you provide three diagrams. (Note: a sketch means that you do not need to draw to scale.) 4) For the critical flow case for B2,c (Part 1), calculate the normal flow depth y3 at a distance downstream of your hump (position 3). The channel is long enough to achieve uniform flow conditions. What is the Froude number at position 3? 5) For the critical flow case for B2,c (Part 1), classify your free-surface profile [gradually varied, rapidly varied and uniform flow] and sketch your free-surface profile along the channel, including all the relevant features. Indicate the different flow regimes (i.e. supercritical, critical or subcritical flow) along the channel. 6) State and explain two of the assumptions involved in writing the following equation: v12 v22 z1+y1 + 2g = z2 + y2 + 2g Where z is the elevation of the channel bed, y is the water depth, v the average flow velocity and g is the gravity acceleration; the subscripts 1 and 2 represent the respective points in the channel. Please note that, if you address more than two assumptions, only the first two will be considered for marking purposes.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mechanical engineering questions
-
Two waves, y1 (t) and y2 (t), have identical amplitudes and oscillate at the same frequency, but y2 (t) leads y1 (t) by a phase angle of 60o. If y1 (t) = 4cos (2 x 103t) write down the expression...
-
In each case find new variables y1 and y2 that diagonalize the quadratic form q. (a) q = x21 + 6x1x2 + x22 (b) q = x21 + 4x1x2 - 2x2
-
In Problem 7(a), let y1 and y2 be the dual variables. Determine the following pairs of primal-dual solution are optimal: (a) (x1 = 3, x2 = 1; y1 = 4, y2 = 1) (b) (x1 = 4, x2 = 1; y1 = 1, y2 = 0) (c)...
-
Segment Analysis Winston Sylvester Corporation is a brokerage and financial service company. The company recently provided information about its major business segments as follows (in millions):...
-
Evaluate Keller-Globes approach to training.
-
Sea-level standard air is sucked into a vacuum tank through a nozzle, as in Fig. P9.63. A normal shock stands where the nozzle area is 2 cm2, as shown. Estimate (a) The pressure in the tank; and (b)...
-
How does cross-cultural evidence raise questions about the division of humanity into male and female?
-
Consider the following mixed-integer linear program: Max 2x1 + 3x2 s.t. 4x1 + 9x2 36 7x1 + 5x2 35 x1, x2 0 and x1 integer a. Graph the constraints for this problem. Indicate on your graph all...
-
Normalize the given ERD diagram This is my attempt. I would like to know if it is correct and if not for it to be corrected. PROFESSOR PK PROF ID INTEGER PROF LNAME VARCHAR(50) PROF FNAME...
-
John Parsons (123-45-6781) and George Smith (123-45-6782) are 70% and 30% owners, respectively, of Premium, Inc. (11-1111111), a candy company located at 1005 16th Street, Cut and Shoot, TX 77303....
-
I have to Demonstrate professional communication in the content and presentation of your submission and I'm wonder how do I go about it this my first time do this so Im a little lost. If Im wrong...
-
Compare and contrast the different memory technologies discussed in this chapter as they pertain to embedded real - time systems.
-
What does the term unsubstantiated bug mean? What should analysts do when an unsubstantiated bug is found?
-
In general terms, suggest a possible scheme that would allow a machine - language instruction to be interruptible. What would be the overall effect on instruction s execution time and CPU s...
-
What is system support?
-
You are designing the architecture of a high - performance CPU for hard real - time applications. List and justify the principal architectural selections that you would make.
-
Create a dataset to build a model to predict "price" as the target variable for Broward County, Florida, United States. Decide which columns might be useful for modeling. Hide and exclude any column...
-
For the following exercises, write the first four terms of the sequence. a n = 2 n 2
-
JoShop uses lathes and drill presses to produce four types of machine parts, PP1, PP1, PP3, and PP4. The table below summarizes the pertinent data. Machining time in minutes per wnvit o Pi PP2 P3 P...
-
A company that operates 10 hours a day manufactures two products on three sequential processes. The following table summarizes the data of the problem: Determine the optimal mix of the two products....
-
In the TOYCO model, suppose that the company can reduce the unit times on operations 1, 2, and 3 for toy trains from the current levels of 1, 3, and 1 minutes to .5, 1, and .5 minutes, respectively....
-
Using the fourth-order Runge-Kutta method, solve Problem 11.15. Data From Problem 11.15:- Using the second-order Runge-Kutta method, solve the differential equation \(\ddot{x}+1000 x=0\) with the...
-
Using the central difference method, find the response of the two-degree-of-freedom system shown in Fig. 11.2 when \(c=2, F_{1}(t)=0, F_{2}(t)=10\). Figure 11.2:- X1(t) -x2(t) F(1) k=2 -F2(t) k = 4...
-
Using the central difference method, find the response of the system shown in Fig. 11.2 when \(F_{1}(t)=10 \sin 5 t\) and \(F_{2}(t)=0\). Figure 11.2:- X1(t) -x2(t) F(1) k=2 -F2(t) k = 4 k2=6 00000...
Study smarter with the SolutionInn App