Question

Question 2. For medical applications the volume flowrate Q through a small needle can be approximated to depend on the needle radius R, the drug viscosity ?, and the pressure drop per unit needle length ($dp/dx$), i.e. $Q = f(R, ?, \frac{dp}{dx})$. Treating the variable ($dp/dx$) as a single variable, answer the following: (a) Determine the total number of parameters in the problem. Write the dimensions for each of the parameters in terms of primary dimensions. [2 marks] (b) List all the primary dimensions represented in the problem. [1 mark] (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) Generate a non-dimensional relationship between the parameters. Show all your work. [10 marks] (e) Explain which well-known law the relationship found above resembles to. Based on this, what is the value of the constant in the relationship? [10 marks]

          Question 2. For medical applications the volume flowrate Q through a small needle
can be approximated to depend on the needle radius R, the drug viscosity ?, and the
pressure drop per unit needle length ($dp/dx$), i.e.
$Q = f(R, ?, \frac{dp}{dx})$.
Treating the variable ($dp/dx$) as a single variable, answer the following:
(a) Determine the total number of parameters in the problem. Write the dimensions
for each of the parameters in terms of primary dimensions.
[2 marks]
(b) List all the primary dimensions represented in the problem.
[1 mark]
(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) Generate a non-dimensional relationship between the parameters. Show all
your work.
[10 marks]
(e) Explain which well-known law the relationship found above resembles to.
Based on this, what is the value of the constant in the relationship?
[10 marks]

Question 2. For medical applications the volume flowrate Q through a small needle
can be approximated to depend on the needle radius R, the drug viscosity ?, and the
pressure drop per unit needle length (dp/dx), i.e.
Q = f(R, ?, (dp)/(dx)).
Treating the variable (dp/dx) as a single variable, answer the following:
(a) Determine the total number of parameters in the problem. Write the dimensions
for each of the parameters in terms of primary dimensions.
[2 marks]
(b) List all the primary dimensions represented in the problem.
[1 mark]
(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) Generate a non-dimensional relationship between the parameters. Show all
your work.
[10 marks]
(e) Explain which well-known law the relationship found above resembles to.
Based on this, what is the value of the constant in the relationship?
[10 marks]

Added by Stephen C.

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