Figure 6.31 shows a de-aerator operated at 381 mm Hg vacuum. (Atmospheric pressure is 762 mm H

step 1 All right, so we're able to solve part A here from the information alone. So for the flow rate,

Figure 6.31 shows a de-aerator operated at 381 mm Hg...

Figure 6.31 shows a de-aerator operated at $381 \mathrm{~mm} \mathrm{Hg}$ vacuum. (Atmospheric pressure is $762 \mathrm{~mm} \mathrm{Hg}$.) It is desired to allow a positive suction flow into the pump. If the fluid has a density of $1040 \mathrm{~kg} / \mathrm{m}^3$, the flow rate is $40 \mathrm{~L} / \mathrm{min}$, and the pipe is 1.5 -in. sanitary pipe, calculate the height " $h$ " the bottom of the de-aerator must be set above the pump level in order that the pressure at the pump intake is at least $5 \mathrm{kPa}$ above atmospheric pressure. The fluid is Newtonian and has a viscosity of 100 centipoises. [Note: Total length of straight pipe from first elbow below the pump to the entrance to the pump $=4 \mathrm{~m}$. Distance from pump level to horizontal pipe $=0.5 \mathrm{~m}$.]

Figure 6.31 shows a de-aerator operated at $381 \mathrm{~mm} \mathrm{Hg}$ vacuum. (Atmospheric pressure is $762 \mathrm{~mm} \mathrm{Hg}$.) It is desired to allow a positive suction flow into the pump. If the fluid has a density of $1040 \mathrm{~kg} / \mathrm{m}^3$, the flow rate is $40 \mathrm{~L} / \mathrm{min}$, and the pipe is 1.5 -in. sanitary pipe, calculate the height " $h$ " the bottom of the de-aerator must be set above the pump level in order that the pressure at the pump intake is at least $5 \mathrm{kPa}$ above atmospheric pressure. The fluid is Newtonian and has a viscosity of 100 centipoises.
[Note: Total length of straight pipe from first elbow below the pump to the entrance to the pump $=4 \mathrm{~m}$. Distance from pump level to horizontal pipe $=0.5 \mathrm{~m}$.]

Key Concepts

Pipe Flow and Flow Regime

Pipe flow analysis involves the study of how fluids move through conduits, where parameters such as flow rate, pipe diameter, and fluid properties determine the flow regime, be it laminar or turbulent. The flow regime affects the friction factor and, consequently, the head losses in the pipe. Understanding whether a flow is laminar or turbulent is crucial for accurate prediction of pressure drops and designing systems that meet specific pressure requirements.

Newtonian Fluid Behavior and Viscosity

The behavior of Newtonian fluids is characterized by a constant viscosity that does not change with the rate of shear. This property simplifies the analysis of fluid flow, as the viscous effects remain predictable regardless of the flow conditions. In engineering applications, the known constant viscosity enables the use of standard equations for calculating head loss, flow rate, and determining the flow regime, which are all critical to system design and analysis.

Pump Suction Requirements

Pump suction requirements involve ensuring that the pressure at the pump inlet remains within a range that prevents cavitation and maintains efficient operation. In many systems, particularly those operating under vacuum or low-pressure conditions, it is important to provide a sufficient positive inlet pressure (or pressure head) at the pump to avoid operational issues. This requirement often necessitates adjustments in the elevation or configuration of connected components.

Hydrostatic Pressure

This concept involves the relationship between the pressure in a fluid and the height (or depth) of the fluid column. In many fluid mechanics applications, including systems with elevation differences, the pressure change due to gravity is calculated using the hydrostatic pressure equation, which relates pressure to the product of fluid density, gravitational acceleration, and height. This relationship is critical when adjusting system parameters to achieve required pressure conditions at different points in a fluid system.

Frictional Head Loss (Darcy-Weisbach Equation)

Frictional head loss represents the loss of pressure due to the viscous effects of fluid flow within pipes. The Darcy-Weisbach equation is commonly used to estimate these losses and takes into account factors such as the length of the pipe, the fluid velocity, the pipe diameter, and the friction factor, which itself may depend on the flow regime. Accurately calculating friction losses is essential when assessing how much additional head is needed to overcome resistances in the piping system.

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