Lecture 2 example, single tank hydraulic system (ENGR5001)

Lecture 2 example, single tank hydraulic systemTutorialCurrent spec2:210 min

ENGR5001 Lecture 2 worked example 5, single tank hydraulic system (slides 26-28)

A tank of constant cross-sectional area $A$ is filled at volumetric flow rate $Q_i$ and drains through an orifice near the base at flow rate $Q_o$ . The liquid depth above the orifice is $h$ (see figure).

Single tank of area A, inflow Q_i at the top, head h, outflow Q_o through an orifice.

Formulas you may need

Conservation of volume (mass) for an incompressible fluid: $A\dfrac{dh}{dt} = Q_i - Q_o$ (learn this)
Linear outflow assumption $Q_o = K'h$ (learn this)
Generalised first order form $\tau\dfrac{dx}{dt} + x = Ku(t)$ (learn this)

(a)
State the assumptions used in the lecture model.
(b)
Derive a linear model relating the outflow $Q_o$ to the inflow $Q_i$ .
(c)
Put it into generalised first order form and give the time constant and steady state gain.