A theory is presented for time-dependent two-layer hydraulic flows thr
ough straits. The theory is used to study exchange flows forced by a p
eriodic barotropic (tidal) flow. For a given strait geometry the resul
ting flow is a function of two nondimensional parameters, gamma = (g'H
)T-1/2/L and q(b0) = u(b0)/(g'H)(1/2). Here g', H, L, T, and u(b0) are
, respectively, the reduced gravity, strait depth and length scales, t
he forcing period, and the barotropic velocity amplitude; gamma is a m
easure of the dynamic length of the strait and q(b0) a measure of the
forcing strength. Numerical solutions for both a pure contraction and
an offset sill-narrows combination show that the exchange flow, averag
ed over a tidal cycle, increases with qb0 for a fixed gamma. For fixed
q(b0) the exchange increases with increasing gamma. The maximum excha
nge is obtained in the quasi-steady limit gamma --> infinity. The mini
mum exchange is found for gamma --> 0 and is equal to the unforced ste
ady exchange. The usual concept of hydraulic control occurs only in th
ese two limits of gamma. In the time-dependent regime complete informa
tion on the strait geometry, not just at a finite number of control po
ints, is required to determine the exchange. The model results are com
pared to laboratory experiments for the pure contraction case. Good ag
reement for both interface evolution and average exchange is found if
account is made for the role of mixing, which acts to reduce the avera
ge salt (density) transport. The relevance of these results to ocean s
traits is discussed. It is shown that many typical straits lie in the
region of parameter space where time dependence is important. Applicat
ion to the Strait of Gibraltar helps explain the success of the unforc
ed steady hydraulic theory.