Question 10 of 13: HGL and EGL Profiles Along the Island Bend Dam Spillway

Question 10: HGL and EGL Profiles Along the Island Bend Dam Spillway (5 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

This is a descriptive/graphical Section B question: the reasoning below both describes the requested profile and doubles as the "drawing," reproduced as an inline sketch.

(a) Water surface. Upstream of the dam the surface is essentially flat at F.S.L. (reservoir, negligible approach velocity). As the flow is drawn toward and over the open gate/crest it accelerates and the surface drops noticeably (energy converts from pressure/elevation head to velocity head). Down the steep spillway chute the flow is thin, fast, and supercritical, hugging close to the invert. Near the toe of the spillway, where the steep chute meets the flatter downstream channel, a hydraulic jump forms: the surface abruptly rises through a turbulent, foaming transition back to a slower, deeper subcritical flow, which then gradually settles toward the normal tailwater level well downstream.

(b) HGL (hydraulic grade line). For open-channel flow the HGL coincides with the water surface itself (piezometric head = surface elevation, since the pressure at the free surface is atmospheric = gauge zero throughout). So the HGL traces exactly the profile described in (a): flat in the reservoir, dropping over the crest, low and roughly parallel to the chute invert down the spillway, jumping up abruptly at the hydraulic jump, then leveling out in the tailwater reach.

(c) EGL (energy grade line). The EGL sits above the HGL by the local velocity head V²/2g. In the still reservoir this gap is negligible, so EGL ≈ HGL ≈ F.S.L. As the flow accelerates over the crest and down the chute, V²/2g grows rapidly, so the EGL separates further and further above the (now much lower) water surface even while the EGL itself is continuously, gently falling (a small, steady loss to spillway-surface friction). Across the hydraulic jump the EGL drops sharply and discontinuously — this abrupt EGL drop IS the turbulent energy dissipated in the jump. Downstream, with velocity head small again, EGL and HGL converge back to nearly the same level, both gently falling toward the tailwater slope's friction loss.

(d) Explanation of each transition. Every place the profile bends is a place where velocity or direction changes:

• Approach → crest: the channel narrows/steepens as flow is drawn toward the gate; by continuity the velocity must rise, so (by Bernoulli/energy conservation, since losses here are small) the surface must drop to supply that kinetic energy — this is a smooth, loss-free acceleration, so the EGL barely drops here even though the water surface (HGL) drops a great deal.
• Crest → chute: gravity continues to accelerate the thin sheet of water down the steep face; the flow passes through critical depth at (or near) the crest and becomes supercritical on the chute, explaining why the surface stays thin and fast rather than recovering.
• Chute → tailwater (the hydraulic jump): a supercritical flow cannot smoothly decelerate back to the slower subcritical tailwater condition required farther downstream; the only mechanism available is a turbulent hydraulic jump, which dissipates the excess kinetic energy as heat/turbulence — visible as the sharp, discontinuous EGL drop and a sudden rise in the water surface.
• Tailwater reach: once subcritical and reasonably uniform, the small continued EGL/HGL slope simply reflects ordinary friction loss along the channel bed, with velocity essentially constant.