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Question 2. A weir is an obstruction in a channel flow which can be calibrated to measure the flowrate, see Figure 2. The volume flowrate Q varies with acceleration due to gravity g, weir width b (into the paper), and upstream water height H above the weir crest, i.e. $Q = f(g, b, H)$. Answer the following: (a) Determine the number of parameters (n) in the problem. Write the dimensions (in terms of primary dimensions) for each of the parameters. [5 marks] (b) List all the primary dimensions represented in the problem? [2 marks] (c) If the reduction (j) was set to the number of primary dimensions represented in the problem, what is the expected number of non-dimensional parameters? [2 marks] (d) Without choosing weir width b as a repeating parameter, generate a non- dimensional relationship between the parameters. Show all your work. [16 marks] (e) If it is known that Q is proportional to b obtain a unique functional relationship between the parameters. [5 marks] Weir width b into the plane. H Q Weir Figure 2 (TOTAL 30 MARKS)

          Question 2. A weir is an obstruction in a channel flow which can be calibrated to
measure the flowrate, see Figure 2. The volume flowrate Q varies with acceleration
due to gravity g, weir width b (into the paper), and upstream water height H above
the weir crest, i.e. $Q = f(g, b, H)$. Answer the following:
(a) Determine the number of parameters (n) in the problem. Write the dimensions
(in terms of primary dimensions) for each of the parameters.
[5 marks]
(b) List all the primary dimensions represented in the problem?
[2 marks]
(c) If the reduction (j) was set to the number of primary dimensions represented
in the problem, what is the expected number of non-dimensional parameters?
[2 marks]
(d) Without choosing weir width b as a repeating parameter, generate a non-
dimensional relationship between the parameters. Show all your work.
[16 marks]
(e) If it is known that Q is proportional to b obtain a unique functional relationship
between the parameters.
[5 marks]
Weir width b into the plane.
H
Q
Weir
Figure 2
(TOTAL 30 MARKS)

Question 2. A weir is an obstruction in a channel flow which can be calibrated to
measure the flowrate, see Figure 2. The volume flowrate Q varies with acceleration
due to gravity g, weir width b (into the paper), and upstream water height H above
the weir crest, i.e. Q = f(g, b, H). Answer the following:
(a) Determine the number of parameters (n) in the problem. Write the dimensions
(in terms of primary dimensions) for each of the parameters.
[5 marks]
(b) List all the primary dimensions represented in the problem?
[2 marks]
(c) If the reduction (j) was set to the number of primary dimensions represented
in the problem, what is the expected number of non-dimensional parameters?
[2 marks]
(d) Without choosing weir width b as a repeating parameter, generate a non-
dimensional relationship between the parameters. Show all your work.
[16 marks]
(e) If it is known that Q is proportional to b obtain a unique functional relationship
between the parameters.
[5 marks]
Weir width b into the plane.
H
Q
Weir
Figure 2
(TOTAL 30 MARKS)

Added by Yvonne H.

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