Solution
= Solution
The net axial pressure force on a length-$L$ fluid cylinder is
$$
F_p
=\pi R^2[p(z_0)-p(z_0+L)]
=-\pi R^2L\frac{\partial p}{\partial z}.
$$
From part (a),
$$
\mu w'(R)=\frac R2\frac{\partial p}{\partial z}.
$$
Multiplying this wall shear stress by the lateral area $2\pi RL$ gives
$$
F_{\rm wall}
=2\pi RL\,\mu w'(R)
=\pi R^2L\frac{\partial p}{\partial z}.
$$
Consequently
$$
\boxed{F_p+F_{\rm wall}=0},
$$
which is the required steady force balance.