Solution
= Solution
The speeds are $U=q/A$ upstream and $v=q/(2a)$ in either daughter vessel. Bernoulli therefore gives
$$
\boxed{p_{\rm up}-p_{\rm down}=\frac\rho2(v^2-U^2)
=\frac{\rho q^2}{2}\left(\frac1{4a^2}-\frac1{A^2}\right).}
$$
= Solution
The speeds are $U=q/A$ upstream and $v=q/(2a)$ in either daughter vessel. Bernoulli therefore gives
$$
\boxed{p_{\rm up}-p_{\rm down}=\frac\rho2(v^2-U^2)
=\frac{\rho q^2}{2}\left(\frac1{4a^2}-\frac1{A^2}\right).}
$$