Abstract
In the present study, a practical method is developed to predict the radial velocity of the flow towards circular and square intakes. It is shown that one single spherical sink surface passing from the desired points that have radial velocity vectors of identical magnitude within the ambient fluid can be used for the prediction of the radial velocity. The specific imaginary center of the corresponding spherical sink surface should be located on the center-line axis downstream of the entrance of the intake. As opposed to the previous studies, the proposed method does not require the solution of equations in closed-integral form, and it can also be used for the orifice-intake not opening into the atmosphere (submerged outlet), and an intake with a pipe, or intake-pipe projecting into the ambient fluid. It is shown that velocity field can be predicted with the introduced method even in the case of circulation imposed or induced ambient fluid flow. The agreement between the theoretical results and the available experimental/numerical results was found to be good.
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Abbreviations
- A :
-
Intake-entrance cross-section area
- a :
-
Side-dimension of a square intake-entrance
- A s :
-
Net effective area of the SSS
- A sb :
-
Net effective base area of the SSS
- A slimit :
-
Limit magnitude of As
- D :
-
Internal diameter of a circular intake-entrance
- h :
-
Altitude of the spherical sector (cap) of the SSS remaining above the fluid surface
- l :
-
Distance between Co (center of the intake entrance) and C (center of SSS)
- l limit :
-
Limit magnitude of l
- MAE:
-
Mean average error
- MPE:
-
Mean percentage error
- MSE:
-
Mean square error
- Q :
-
Intake discharge
- Q s :
-
Discharge through the SSS
- R :
-
Horizontal distance to the vertical central axis of the intake-entrance
- r :
-
Radius of SSS
- R * :
-
Correlation coefficient
- RMSE:
-
Root mean square error
- r limit :
-
Limit magnitude of r
- r sb :
-
Radius of the base of the SSS for the case of SSS ≤ SSSlimit
- S :
-
Submergence of the center Co of the intake entrance
- SS:
-
Spherical sink
- SSS:
-
Spherical sink surface
- SSSlimit :
-
Limit SSS
- SPS:
-
Single point sink
- V :
-
Average intake velocity
- V s :
-
Radial velocity at SSS
- V slimit :
-
Limit magnitude of Vs
- x :
-
Distance of the intersection point B of the SSS and the central-axis line of the intake-entrance to Co
- x limit :
-
Limit magnitude of x
- α :
-
Slope angle of the radial line connecting P on SSS and C (center of SSS)
- η :
-
Vertical distance of the point P on SSS to the bottom boundary
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The authors would like to thank Gazi University Academic Writing Application and Research Center for proofreading the article.
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Yıldırım, N., Taştan, K. Velocity Distribution Upstream of Circular and Square Intakes. KSCE J Civ Eng 28, 197–208 (2024). https://doi.org/10.1007/s12205-023-0941-z
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DOI: https://doi.org/10.1007/s12205-023-0941-z