Preliminary design for a tidal turbine siting requires us to find the flow characteristics over a river bed. Bathymetry data of the tidal channel indicates that the bed has a dune as shown in the figure below. In 2D potential flow, the flow over this dune can be modelled using a particular streamline of flow past a cir- cular cylinder that can be constructed by superposition of an incoming uniform flow with streamwise speed of U = 1 m/s and a doublet of strength K = = 2π m³/s. The streamline that represents the dune is one that passes through (x,z) (0, aR) where R √K/(2TU) is the radius of the circular cylinder. = = Use a = 1.2 (i) Determine an equation for the streamline that repre- sents the dune. Provide your answer in terms x, z and a (or use its numerical value). (ii) Plot the dune and the streamlines around it using the potential flow code provided in your lecture materials.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!

Q2.
Preliminary design for a tidal turbine siting requires us to
find the flow characteristics over a river bed. Bathymetry
data of the tidal channel indicates that the bed has a
dune as shown in the figure below.
In 2D potential flow, the flow over this dune can be
modelled using a particular streamline of flow past a cir-
cular cylinder that can be constructed by superposition
of an incoming uniform flow with streamwise speed of
U = 1 m/s and a doublet of strength K 2π m³/s. The
streamline that represents the dune is one that passes
through (x,z)
(0, aR) where R
radius of the circular cylinder.
-
S.
√K/(2TU) is the
=
1.2
-
Use a =
(i) Determine an equation for the streamline that repre-
sents the dune. Provide your answer in terms x, z and a
(or use its numerical value).
(ii) Plot the dune and the streamlines around it using the
potential flow code provided in your lecture materials.
Transcribed Image Text:Q2. Preliminary design for a tidal turbine siting requires us to find the flow characteristics over a river bed. Bathymetry data of the tidal channel indicates that the bed has a dune as shown in the figure below. In 2D potential flow, the flow over this dune can be modelled using a particular streamline of flow past a cir- cular cylinder that can be constructed by superposition of an incoming uniform flow with streamwise speed of U = 1 m/s and a doublet of strength K 2π m³/s. The streamline that represents the dune is one that passes through (x,z) (0, aR) where R radius of the circular cylinder. - S. √K/(2TU) is the = 1.2 - Use a = (i) Determine an equation for the streamline that repre- sents the dune. Provide your answer in terms x, z and a (or use its numerical value). (ii) Plot the dune and the streamlines around it using the potential flow code provided in your lecture materials.
Power extraction of a tidal turbine in preliminary design is
typically calculated by using the velocities obtained from
potential flow. In such calculations, the relative change
in power extraction due to the presence of the dune can
be represented as,
ACP
where U (= √u² + w²
along the dune.
=
=
U³
U3
u²+u) is the local speed
-
1
Transcribed Image Text:Power extraction of a tidal turbine in preliminary design is typically calculated by using the velocities obtained from potential flow. In such calculations, the relative change in power extraction due to the presence of the dune can be represented as, ACP where U (= √u² + w² along the dune. = = U³ U3 u²+u) is the local speed - 1
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