Hydraulic Jump Stilling Basin

Overview

  • Context: This study guide focuses on the hydraulic jump stilling basin as discussed in Example 4b-1 from the course CE 415 at the University of Saskatchewan.

  • Reference Material: Sturm, T.W. (2001). Open Channel Hydraulics. McGraw-Hill Higher Education. Reference for electronic version: Sturm, T.W. (2021). Open Channel Hydraulics (3rd Edition). McGraw-Hill Companies, New York, NY. ISBN 9781260469707.

Problem Statement

  • Situation:

    • A spillway of width 40 ft discharges 10,000 cfs (cubic feet per second) into a stilling basin of the same width.

    • Elevation of lake level behind the spillway: 200 ft

    • Elevation of river water surface downstream of the stilling basin: 100 ft

  • Assumption: A 10% energy loss occurs as water flows down the spillway.

  • Objective: Determine the invert elevation of the floor of the stilling basin to ensure the formation of a hydraulic jump. Also, select the appropriate U.S. Bureau of Reclamation (USBR) stilling basin design and provide a sketch showing all dimensions.

Hydraulic Jump Fundamentals

  • Hydraulic Jump: A rapid transition in flow conditions that occurs when supercritical flow transitions to subcritical flow, leading to an increase in water surface elevation and energy loss.

Stable Basin Design

  • Type of Stilling Basin: Required design is a Type 2 Stilling Basin.

  • Design Parameters:

    • $ ext{Velocity entering basin} = 83 ext{ ft/s}$

    • $ ext{Froude Number} (Fr) = 8.45$

Froude Number Classification for Stilling Basins

  • Froude Number Range & Basin Type:

    1. 1.7 to 2.5

    • Type: 1

    • Comments: No chute, basin blocks, or sill needed. The jump formed is weak.

    1. 2.5 to 4.5

    • Type: 4

    • Comments: Chute blocks and end sill included, no baffle blocks. Transition jump, inflow jet unstable with considerable wave action.

    1. Greater than 4.5

    • Type: 2 or 3

    • Comments: Type 3 includes baffle blocks and limits inflow velocities to less than 60 ft/s (18.29 m/s).

Recommended Dimensions for Stillings Basin

  • Parameters for Type 2 Stilling Basin:

    • Diameter of chute blocks (D1):

    • Height and Width (y1):

      • $D_1 = y_1 = 3.01 ext{ ft}$

    • Diameter of end sill (D2):

    • Height and Width (y2):

      • $D_2 = y_2 = 34.45 ext{ ft}$

Chute Block Specifications

  • Chute Block Offset from Wall:

    • $ rac{D_1}{2} = 1.51 ext{ ft}$

  • Width of chute block:

    • $D_1 = 3.01 ext{ ft}$

  • Height of chute block:

    • $3.01 ext{ ft}$

  • Spacing between chute blocks:

    • $3.01 ext{ ft}$

End Sill Block Specifications

  • Spacing between end sills:

    • $0.15D_2 = 5.17 ext{ ft}$

  • Width of end sill block:

    • $0.15D_2 = 5.17 ext{ ft}$

  • Height of end sill block:

    • $0.2D_2 = 6.89 ext{ ft}$

Chute Block Positioning

  • Positioning Options:

    • Centreline positions:

    • Option 1: $0.435 ext{ ft}$

    • Option 2: $0.349 ext{ ft}$

Tailwater Recommendations

  • Tailwater Depth Recommendation:

    • Should be calculated as:

    • $1.05y_2$, where adjustments may be needed to reduce z and iteration of the design.

Length Dependency

  • Design Aspect:

    • Length of the basin depends on the value of $y_2$.