Marwa F. Shaheen

Piano key weirs (PKWs) provide high discharge efficiency within a limited footprint, but the influence of inlet- and outlet-key shapes on their energy dissipation has received limited attention. This study investigates the effects of curved inlet- and outlet-key geometries on PKW energy dissipation using 102 free-flow experimental runs. Nine configurations are tested: a linear reference (M1) and C-shaped, inverted C-shaped, S-shaped, and inverted S-shaped modifications applied separately to the inlet and outlet keys. A FLOW-3D HYDRO model is validated against the measurements, reproducing the total head with R² = 0.997 and RMSE = 0.0013 m and the relative energy loss within ±15% (MAPE = 6.70%), and is then used to evaluate a combined configuration (M10) with C-shaped inlet and outlet keys. Experimental results show that the relative energy loss decreases with increasing total head ratio, from approximately 71–74% at low heads to 46–52% at higher heads. At H_T/P = 0.18, the C-shaped inlet (M4) and outlet (M5) increase the relative energy loss by 12.80% and 8.27%, respectively, relative to M1. Compared with the numerically simulated M1, M10 is predicted to increase the relative energy loss by 5.86%, 9.64%, and 14.61% at H_T/P = 0.08, 0.12, and 0.18, respectively. A logarithmic relationship fitted to 11 numerical runs is provided for estimating the relative energy loss of M10 within H_T/P = 0.075–0.266. The results show that PKW energy dissipation depends strongly on curvature shape, orientation, and key location.

Piano key weirs (PKWs) increase the effective crest length and provide high discharge capacity within limited spillway widths; however, their hydraulic efficiency depends on key geometry. Addressing the limited understanding of key-curvature effects, this study systematically investigates the influence of inlet- and outlet-key curvature on the discharge coefficient (C_d) and crest-wise discharge distribution of type-A PKWs. Nine configurations are examined experimentally in a flume at the Hydraulics Research Institute, Egypt. These include a reference model with linear inlet and outlet keys and modified geometries incorporating C- and S-shaped keys in both normal and inverted forms. Experiments are conducted under free-flow conditions for total-head ratios H_T/P up to 0.23, where H_T is the total upstream head above the crest and P is the PKW height. A three-dimensional numerical model using FLOW-3D HYDRO is validated against these experimental data and subsequently extended to H_T/P ≈ 0.50–0.60. All reported results and conclusions are based on the numerical simulations over the full investigated range. Results show that C_d increases to a peak near H_T/P ≈ 0.08 and then decreases gradually for all configurations. Both inlet- and outlet-key curvature influence hydraulic performance by modifying flow guidance and redistribution along the crest. However, only the inverted C-shaped inlet configuration (M2) improves efficiency, increasing C_d by about 5.46% on average over the investigated head range and enhancing the total discharge by approximately 4.36% at H_T/P ≈ 0.12 relative to the reference case. Discharge-distribution analysis indicates that this improvement results from inlet feeding and efficient flow conveyance along the sidewall crest. A predictive relation is developed for the optimal configuration to support hydraulic design.

Aquatic vegetation can influence hydraulic performance in channels, rivers, and floodplains. Most previous studies used cylindrical stems to simulate vegetation, while few studies used shrub-like or sedge structures that exhibited a maximum width near the top of the vegetation. In contrast, this research focuses on shrub-like structures that show a maximum width near the bottom of the vegetation. To understand the effects of aquatic vegetation on velocity distribution, water surface profile, and energy loss, experiments have been conducted in an open channel with a rectangular cross-section. The results indicated that the streamwise velocity within the lower layer remains nearly constant with depth where z/y is less than 0.20. However, once z/y exceeds 0.20, the streamwise velocity increases rapidly as the depth increases toward the water surface. Additionally, the shape of the vegetation influences the position of the inflection point. Moreover, the water level rises upstream of the vegetated area, decreases within it, and gradually returns to the normal depth downstream. The bed slope has little effect on relative energy loss, with maximum values reaching 6.61%, while the presence of vegetation leads to a significant increase, reaching up to 22.51%. The relative energy loss increases with a higher submerged ratio. A new empirical equation is proposed to estimate the relative energy loss in vegetated channels.

Aquatic vegetation can influence hydraulic performance in channels, rivers and floodplains. Most previous studies used cylindrical stems to simulate vegetation, while few studies used shrub-like or sedge structures that exhibited a maximum width near the top of the vegetation. In contrast, this research focuses on shrub-like structures that show a maximum width near the bottom of the vegetation. To understand the effects of aquatic vegetation on velocity distribution, water surface profile, and energy loss, experiments have been conducted in an open channel with a rectangular cross-section. The results indicated that the streamwise velocity within the lower layer remains nearly constant with depth where z/y is less than 0.20. However, once z/y exceeds 0.20, the streamwise velocity increases rapidly as the depth increases toward the water surface. Additionally, the shape of the vegetation influences the position of the inflection point. Moreover, the water level rises upstream of the vegetated area, decreases within it, and gradually returns to the normal depth downstream. The bed slope has little effect on relative energy loss, with maximum values reaching 6.61%, while the presence of vegetation leads to a significant increase, reaching up to 22.51%. The relative energy loss increases with a higher submerged ratio. A new empirical equation is proposed to estimate the relative energy loss in vegetated channels.