Sure, let's find the expression for the viscosity \(\eta\) from the given equation. The given formula is:
[tex]\[
\frac{v}{t} = \pi \frac{(P1 - P2)}{8 \eta L}
\][/tex]
We need to isolate \(\eta\) on one side of the equation:
### Step 1: Multiply both sides of the equation by \(8 \eta L\)
Doing this will help get \(\eta\) out of the denominator on the right-hand side.
[tex]\[
8 \eta L \cdot \frac{v}{t} = \pi (P1 - P2)
\][/tex]
### Step 2: Divide both sides by \(8 \left(\frac{v}{t}\right) L\)
To isolate \(\eta\), we divide both sides by \(8 \left(\frac{v}{t}\right) L\):
[tex]\[
\eta = \frac{\pi (P1 - P2)}{8 \left(\frac{v}{t}\right) L}
\][/tex]
### Final Expression
We have successfully isolated \(\eta\):
[tex]\[
\eta = \pi \frac{(P1 - P2)}{8 \left(\frac{v}{t}\right) L}
\][/tex]
So the expression for the viscosity \(\eta\) in terms of the given variables is:
[tex]\[
\eta = \pi \frac{(P1 - P2)}{8 \left(\frac{v}{t}\right) L}
\][/tex]
