Q1: The formula used for determining flow velocities in sewers, is known as

ANS:D - Manning's formula.

Manning's formula, named after the Irish engineer Robert Manning, is an empirical equation used to calculate the velocity of flow in an open channel, such as rivers, streams, canals, or sewers. It is widely used in hydraulic engineering and fluid mechanics for estimating flow rates and designing hydraulic structures. Manning's formula is particularly useful for situations where the flow conditions are steady and the channel geometry is well-defined. The basic form of Manning's formula is: V=1/n ​⋅R^2/3⋅S^1/2 Where:

• V is the velocity of flow (in meters per second).
• n is the Manning's roughness coefficient or rugosity coefficient (dimensionless). This coefficient represents the resistance to flow offered by the channel bed and banks. It depends on factors such as channel roughness, vegetation, sediment, and alignment.
• R is the hydraulic radius or hydraulic mean depth (in meters). It is calculated as the cross-sectional area of flow divided by the wetted perimeter. Hydraulic radius is a measure of the flow area relative to the wetted perimeter and is used to account for the channel shape.
• S is the slope of the channel bed (dimensionless). It represents the change in elevation per unit horizontal distance and drives the flow by creating a hydraulic gradient.

Manning's formula is based on the principle of conservation of energy, where the kinetic energy of the flowing water is balanced with the potential energy due to the channel slope. The formula incorporates the effects of channel roughness and slope on flow velocity, making it suitable for a wide range of natural and artificial channels. Manning's roughness coefficient (n) is a key parameter in the formula and is typically determined empirically based on the channel type, material, condition, and flow regime. It can be obtained from tables, charts, or empirical relationships based on observed data or laboratory experiments. Overall, Manning's formula provides a simple and practical method for estimating flow velocities in open channels and is widely used in hydraulic engineering applications, including flood modeling, river management, irrigation design, and sewer system design.