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Side intake sketch; trash rack loss

Short answer

A side intake includes trash boom, inclined rack, sill, gate, hoist deck, undersluice and transition. Trash rack loss is Kirschmer's formula h_t = beta(s/b)^(4/3)(V^2/2g) sin theta, with beta 2.42 rectangular, 1.79 circular; add 25-50% for clogging.

Draw a neat sketch of a side intake with all components. How do you calculate the hydraulic loss at the trash rack?

Sketch of a side intake

PLAN
 river ==========================>
   weir |||||||  undersluice
   bank +---------------------+
        |trash rack  | gate   |--> gravel trap --> canal
        +---------------------+

SECTION
  pond ~~~~~~~~~~~~~~~~~~~~~~~~
   boom o  |  rack (75°)  | gate | hoist deck
        ###|##\           |      |
        ###|###\__________|______|======> canal
   sill (1.0-1.5 m above undersluice)
 /////////////////////////////////////////// bed

Components: trash boom, trash rack with rake, intake sill, gate with stop-log slot, hoist deck, flushing undersluice and the transition to the canal.

Head loss at the trash rack (Kirschmer's formula)

ht=β(sb)4/3V22gsin⁡θh_t=\beta\left(\frac{s}{b}\right)^{4/3}\frac{V^2}{2g}\sin\theta

where hth_t is the head loss (m), β\beta the bar shape factor (2.42 for rectangular bars, 1.83 for rectangular bars with a rounded upstream edge, 1.79 for circular bars, 0.76 for streamlined bars), ss the bar thickness, bb the clear spacing between bars, VV the approach velocity (m/s) and θ\theta the angle of the rack from the horizontal.

A rack in service is partly clogged, so the clean-rack loss is increased by a clogging allowance of 25-50%, and this increased loss is used in the design of the intake.

Example: circular bars (β=1.79\beta=1.79) 10 mm thick at 100 mm clear spacing, V=0.8V=0.8 m/s, θ=75∘\theta=75^\circ:

ht=1.79 (0.1)4/30.8219.62sin⁡75∘=1.79×0.0464×0.0326×0.966=0.0026 mh_t=1.79\,(0.1)^{4/3}\frac{0.8^2}{19.62}\sin75^\circ=1.79\times0.0464\times0.0326\times0.966=0.0026\ \text{m}

This is very small, so the loss at a clean rack is negligible.

✓ Answer checked by Claude Opus 5.5 (high effort)

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