Two students are encouraged to submit a single assignment.
Please use assignment cover sheet (included in Assignment folder) Question 1. Continuity and flow (20 marks)
The following is a diagram of a drainage system.
During a storm, the following depths and velocities are recorded in channels A to E. (for the circular pipe calculations refer to Critical Depth of
Pipe sheet in Lecture 5)
a) Assuming a steady state through the drainage system, calculate the flow, Q, in channel F at point G
b) At G, channel F changes from a very shallow slope to a steep slope so that the flow is forced through critical depth, acting as a flow gauge. Calculate the depth and velocity at this point. (Note: Channel F is not a rectangular channel)
Question 2. Energy Equation and Transitions (25 marks)
The figure below shows a hydraulically long 10.0m wide rectangular channel Between sections A, B and C, there is a constriction in the rectangular channel. The constriction starts at section A, the width is at its minimum at section B, then gradually widens back to the 10m width at section C.
Assuming steady state flow conditions, answer the following questions:
a) If the width of the channel at B is 9m, calculate the depth at B and sketch a flow profile through sections A, B, C. Illustrate your calculations with energy graphs. (Don’t forget to check your Froude numbers at each location)
b) If the width of the channel at section B is 7m, show that the constriction chokes the flow. Illustrate your calculations with energy graphs.
c) For the case when section B is 7m wide, sketch the flow profile upstream and downstream of the choke, showing all important depths.
Hint: Because the flow has been choked, you expect the depth at A to increase to provide the energy to push the flow through the choke. You will need to assume critical energy at B and calculate the depth at A using the energy equation. After B, the flow will be supercritical.
Question 3. Critical depth in non-rectangular channel. (15 marks)
In the channel whose cross-section is shown below, calculate the critical depth when the discharge is:
a) 1.9m3/s (assume that this flow remains in the lower triangular section)
b) 12.5m3/s (assume the critical depth occurs within the top section of the channel)
Question 4. Hydraulic Jump calculations (15 marks)
A 4.2m wide rectangular channel, as shown, carries a flow of 13.8m3/s.
At section ?, it is observed that the flow profile goes through a critical depth control above the 0.4m step in the channel base.
a) Calculate the critical energy at section ?.
b) Assuming there is no energy loss between section ? and ?, use the energy equation to find the depth y2, at ?.
c) Just upstream of section ?, a hydraulic jump forms. Use the hydraulic jump formula to calculate the depth y1, at ?
d) Calculate the energy loss through the hydraulic jump.
