A 900 mm diameter conduit 3600 m long is laid at a uniform...

A 900 mm diameter conduit 3600 m long is laid at a uniform slope of 1 in 1500 and connects two reservoirs. When the levels in the reservoirs are low the conduit runs partly full and it is found that a normal depth of $600 \mathrm{mm}$ gives a rate of flow of $0.322 \mathrm{m}^{3} \mathrm{s}^{-1}$ The Chezy coefficient $C$ is given by $K m^{n}$, where $K$ is a constant, $m$ is the hydraulic mean depth and $n=\frac{1}{6} .$ Neglecting losses of head at entry and exit obtain ( $a$ ) the value of $K$ (b) the discharge when the conduit is flowing full and the difference in level between the two reservoirs is $4.5 \mathrm{m}$ \[ \left[(a) 67.6,(b) 0.562 m^{3} s^{-1}\right] \]

A 900 mm diameter conduit 3600 m long is laid at a uniform slope of 1 in 1500 and connects two reservoirs. When the levels in the reservoirs are low the conduit runs partly full and it is found that a normal depth of $600 \mathrm{mm}$ gives a rate of flow of $0.322 \mathrm{m}^{3} \mathrm{s}^{-1}$
The Chezy coefficient $C$ is given by $K m^{n}$, where $K$ is a constant, $m$ is the hydraulic mean depth and $n=\frac{1}{6} .$ Neglecting losses of head at entry and exit obtain ( $a$ ) the value of $K$
(b) the discharge when the conduit is flowing full and the difference in level between the two reservoirs is $4.5 \mathrm{m}$
\[
\left[(a) 67.6,(b) 0.562 m^{3} s^{-1}\right]
\]

Key Concepts

Chezy Formula

The Chezy formula is an empirical relation used in open channel flow to calculate the average velocity of water. It expresses the relationship between the flow velocity, the channel's hydraulic properties (such as hydraulic radius or mean depth), and the channel slope. In its standard form, the formula is written as V = C?(RS), where V is the velocity, C is the Chezy coefficient, R is the hydraulic radius, and S is the slope of the energy grade line. This formula enables engineers to relate geometric and slope parameters to flow conditions in channels.

Hydraulic Mean Depth

Hydraulic mean depth is a characteristic measure defined as the cross-sectional area of the flow divided by the wetted perimeter or the top width of the free surface, depending on the context. It serves as a representative depth in non-rectangular channels, such as circular conduits, to succinctly describe the flow’s hydraulic geometry. This concept is critical when using empirical formulas like the Chezy formula, as it accounts for the effect of channel shape on flow resistance.

Uniform Open Channel Flow

Uniform open channel flow refers to a state where the flow depth, velocity, and energy slope remain constant along the length of the channel. This condition is achieved when the gravitational driving force is precisely balanced by the frictional resistance of the channel. The assumption of uniform flow simplifies the analysis by allowing the use of steady-state equations, like the Chezy formula, to predict flow behavior, making it a fundamental concept in hydraulic engineering.

Continuity Equation

The continuity equation is a basic principle of fluid mechanics asserting that, for an incompressible fluid, the mass flow rate must remain constant along a streamline. In open channel flow, this is expressed as Q = A × V, where Q is the discharge, A is the cross-sectional area of the flow, and V is the average velocity. This relationship is essential for linking the flow rate to the channel's geometric and hydraulic characteristics, ensuring the conservation of mass in the system.

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