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MMLU-Pro / 12204 / The flow through a sluice gate set into a dam is to be investigated by building…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The flow through a sluice gate set into a dam is to be investigated by building a model of the dam and sluice at 1 : 20 scale. Calculate the head at which the model should work to give conditions corresponding to a prototype head of 20 meters. If the discharge from the model under this corresponding head is 0.5 m^3/s, estimate the discharge from the prototype dam. A relationship between a set of physical variables can be stated as a relationship between a set of independent dimensionless groups made up from suitably chosen variables. The variables involved in this problem are Q -- the flow rate, d -- a leading dimension of the sluice, h -- the head over the sluice, \rho -- the mass density of the water, g -- the gravity field intensity and \mu -- the viscosity of water, so that there is some function, f (Q, \rho, g, h, d, \mu) = 0

category

engineering

options

  1. 1200 m^3/s
  2. 550 m^3/s
  3. 500 m^3/s
  4. 750 m^3/s
  5. 894 m^3/s
  6. 800 m^3/s
  7. 1000 m^3/s
  8. 425 m^3/s
  9. 650 m^3/s
  10. 950 m^3/s

src

stemez-FluidMechanics

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Source and history

upstream_id / Original problem ID
12204
task_id
443002aa-df2f-5950-8b72-44efee8ba709
task_key
default--test--12204
task_revision_id
1
config / split
default / test

Official source

initial import