Solved Problems
Example
Problem: Water flows through a horizontal pipe. At point 1, diameter is 150 mm and pressure is 200 kPa. At point 2, diameter is 75 mm and pressure is 100 kPa. Find the flow rate ().
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Example
Problem: A reducing elbow deflects water upward by 60 degrees. mm ( kPa), mm. Discharge m/s. Neglect energy losses. Find the force exerted by the water on the bend.
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Example
Problem 3: Pitot Tube Application
A Pitot-static tube is used to measure the velocity of an airplane. It is connected to a differential pressure gauge which reads . The density of air is . Calculate the velocity of the airplane.
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Example
Problem 4: Pump Power Required
A pump delivers water from a lower reservoir to a higher reservoir. The elevation difference between the reservoir surfaces is . The flow rate is and total head loss in the system is . Calculate the power required by the pump if its efficiency is .
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Case Study 1: Siphon Operations
Context: Siphons use fluid dynamics principles to move liquid over an elevation without a pump.
Application: A siphon works by atmospheric pressure pushing liquid up the tube because of the lower pressure created by liquid falling down the longer leg. Bernoulli's equation can be used to analyze flow and predict the maximum height the siphon can reach before cavitation occurs (when pressure drops below vapor pressure, causing the liquid to boil). Siphons are widely used in irrigation and decanting liquids.
Case Study 2: Cavitation in Propellers
Context: High-velocity flow can lead to severe damage in fluid machinery.
Application: On the suction side of a ship's propeller, flow velocities are very high. According to Bernoulli's principle, this high velocity results in extremely low pressure. If the pressure drops below the vapor pressure of water, vapor bubbles form. When these bubbles are swept into higher pressure regions, they collapse violently, causing micro-jets that pit and erode the metal blades. Engineers must design propeller shapes and operating speeds to minimize this damaging cavitation.