The theoretical time taken by a particle of water to pass between entry and exit of a settling tank is known as

Explanation:

Detention time (t_d):

The time taken by water (or particle of water) from entering to exit, in the settling tank is known as detention time. In other words, detention time refers to the amount of time that water or wastewater remains in the tank for the purpose of settling and separating solids from the liquid.

Velocity of flow (v_f):

Velocity of flow or flow velocity is refers to the speed at which a fluid (such as a liquid or gas) moves through a particular cross-sectional area within a conduit, channel, pipe, or open channel.

\(t_d={L\over v_f}={LBH\over Q}\)

Where L = Length of tank, v_f = flow velocity, B = width of tank, H = height of tank and Q = discharge or flow rate.

Overflow rate:

Overflow rate or surface overflow rate is defined as the ratio of discharge to the surface area of the settling tank (basin), or the volume of water flow per unit of time divided by the surface area of the settling tank (basin).

\(Overflow\, rate={Discharge\,(Q)\over Surface\, area \,(A)}\)

Hence option (2) is the correct answer.