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What will be the dimension of the flow consistency index for a fluid with a flow behaviour index of -1?
- a)N/m2 s2
- b)N/m2 s
- c)N/ms
- d)N/ms2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What will be the dimension of the flow consistency index for a fluid w...
Explanation: The relation between shear stress Z and velocity gradient 
of a fluid is given by 
where A is the flow consistency index and n is the flow behaviour index. If n = -1, A = Z * Unit of Z is N/m2 and is s-1. Thus, the unit of A will be N/m2 s.
of a fluid is given by where A is the flow consistency index and n is the flow behaviour index. If n = -1, A = Z * Unit of Z is N/m2 and is s-1. Thus, the unit of A will be N/m2 s.Most Upvoted Answer
What will be the dimension of the flow consistency index for a fluid w...
Dimension of Flow Consistency Index
Flow behaviour index (n) is a dimensionless parameter that describes the flow characteristics of a fluid. It is defined as the slope of a log-log plot of shear stress (τ) versus shear rate (γ) in a viscometer.
n = log(τ2/τ1) / log(γ2/γ1)
The flow consistency index (k) is a parameter that represents the consistency or thickness of a fluid. It is defined as the shear stress required to produce a unit shear rate.
k = τ / γ
For a fluid with a flow behaviour index of -1, the dimension of the flow consistency index can be determined as follows:
- The flow behaviour index (n) is negative, indicating that the fluid exhibits shear-thinning behaviour, where the viscosity decreases with increasing shear rate.
- The flow consistency index (k) has dimensions of shear stress (N/m2) divided by shear rate (1/s), which can be simplified to Ns/m3 or Pa.s/m3.
- Since the flow behaviour index (n) is negative, the dimensions of the flow consistency index (k) must be raised to the power of (1/n) to obtain the correct units.
- Therefore, the dimension of the flow consistency index for a fluid with a flow behaviour index of -1 is Ns/m3 raised to the power of (-1/-1), which simplifies to N/m2s.
Therefore, option B (N/m2s) is the correct answer.
Flow behaviour index (n) is a dimensionless parameter that describes the flow characteristics of a fluid. It is defined as the slope of a log-log plot of shear stress (τ) versus shear rate (γ) in a viscometer.
n = log(τ2/τ1) / log(γ2/γ1)
The flow consistency index (k) is a parameter that represents the consistency or thickness of a fluid. It is defined as the shear stress required to produce a unit shear rate.
k = τ / γ
For a fluid with a flow behaviour index of -1, the dimension of the flow consistency index can be determined as follows:
- The flow behaviour index (n) is negative, indicating that the fluid exhibits shear-thinning behaviour, where the viscosity decreases with increasing shear rate.
- The flow consistency index (k) has dimensions of shear stress (N/m2) divided by shear rate (1/s), which can be simplified to Ns/m3 or Pa.s/m3.
- Since the flow behaviour index (n) is negative, the dimensions of the flow consistency index (k) must be raised to the power of (1/n) to obtain the correct units.
- Therefore, the dimension of the flow consistency index for a fluid with a flow behaviour index of -1 is Ns/m3 raised to the power of (-1/-1), which simplifies to N/m2s.
Therefore, option B (N/m2s) is the correct answer.
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What will be the dimension of the flow consistency index for a fluid w...
Explanation: The relation between shear stress Z and velocity gradient of a fluid is given by where A is the flow consistency index and n is the flow behaviour index. If n = -1, A = Z * Unit of Z is N/m2 and is s-1. Thus, the unit of A will be N/m2 s.
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