A pump draws water from a storage tank and forces it through a 10 cm-diameter supply…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A pump draws water from a storage tank and forces it through a 10 cm-diameter supply line (section 1) toward an outlet 4.0 m higher (section 2). The pump maintains a steady gauge pressure of 290 kPa in the 10 cm line, and the required volumetric flow rate is 2.0×10−2m3/s. To reduce splash, the pipeline is fitted with a smooth reducer so that the fluid emerges from section 2 with a lower gauge pressure of at least 50 kPa.
Assume the water density is 1.0×103kgm−3, g=9.8ms−2, the flow is steady and incompressible, and internal frictional losses are negligible.
(a) Compute the average speed of the water in the 10 cm supply line.
(b) Derive an expression for the required speed of the water at section 2 that satisfies the pressure requirement.
(c) Using your result from part (b), determine the maximum allowable internal diameter of the pipe at section 2.