The viscous Force acting on a small sphere moving throuh a fluid is given by F=6πηrv.Find [η].
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Answer:
The dimension formula of η is [ML^{-1}T^{-1}][ML
−1
T
−1
] .
Explanation:
Given that,
The viscous force F = 6\pi \eta rvF=6πηrv
Let, F = k\eta rvF=kηrv
\eta=\dfrac{F}{krv}η=
krv
F
....(I)
Here, k=6\pik=6π = dimensionless constant
We know that,
F= [MLT^{-2}]F=[MLT
−2
]
r=[L]r=[L]
v=[LT^{-1}]v=[LT
−1
]
Put the dimension of all element in equation (I)
\eta=\dfrac{F}{krv}η=
krv
F
\eta=\dfrac{ [MLT^{-2}]}{[L][LT^{-1}]}η=
[L][LT
−1
]
[MLT
−2
]
\eta=[ML^{-1}T^{-1}]η=[ML
−1
T
−1
]
Hence, The dimension formula of η is [ML^{-1}T^{-1}][ML
−1
T
−1
] .
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