A square cross-section duct (0.35 m ×0.35 m ×175 m ) is used to convey air (ρ=1.1 kg / m^3) into

step 1 In this question we have to find flow rate delivered to the room. So first, from the energy equa

A square cross-section duct (0.35 m ×0.35 m ×175 m ) is used...

A square cross-section duct $(0.35 \mathrm{m} \times 0.35 \mathrm{m} \times 175$ $\mathrm{m}$ ) is used to convey air $\left(\rho=1.1 \mathrm{kg} / \mathrm{m}^{3}\right)$ into a clean room in an electronics manufacturing facility. The air is supplied by a fan and passes through a filter installed in the duct. The duct friction factor is $f=0.003,$ the filter has a loss coefficient of $K=3 .$ The fan performance is given by $\Delta p=2250-250 Q-$ $150 Q^{2},$ where $\Delta p(P$ a) is the pressure generated by the fan at flow rate $Q\left(\mathrm{m}^{3} / \mathrm{s}\right) .$ Determine the flow rate delivered to the room.

Key Concepts

Fan Performance Curve

A fan performance curve describes the relationship between the flow rate delivered by the fan and the pressure rise it provides. These curves are typically expressed as equations or graphs, which are used to determine the operating point of the fan when it is matched with the system’s pressure losses. Understanding a fan's performance curve is critical for system design and ensuring efficient operation.

Friction Loss in Ducts

In duct and pipe flow problems, friction loss represents the loss of pressure due to the interaction between the flowing fluid and the walls of the duct. This loss is commonly quantified using the Darcy?Weisbach equation, which incorporates the friction factor, duct length, flow velocity, and hydraulic diameter. Understanding friction loss is crucial for accurately predicting the pressure drop in a system.

Loss Coefficient

The loss coefficient is a nondimensional parameter used to characterize additional pressure losses caused by localized elements in the flow, such as filters, bends, or valves. It allows engineers to account for sudden, non-friction-related losses by multiplying it with the dynamic pressure, making it essential for complete system pressure drop calculations.

System Curve

The system curve represents the total pressure losses in a fluid system as a function of the flow rate, combining all sources of losses, including friction and localized losses like those from filters. The intersection of the system curve with the fan performance curve indicates the operating point, where the pressure supplied by the fan equals the pressure drop in the system.

Pressure Balance in Fluid Systems

Pressure balance is the fundamental principle of equating the pressure rise provided by a fan or pump to the pressure drops incurred throughout the system. This equilibrium determines the actual flow rate operating in the system and is essential for designing systems that meet specified performance criteria.

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