In fluid mechanics and process industries, a rotameter is an instrument used to measure which quantity of a flowing fluid?

Introduction / Context:
Many industrial processes involve the controlled movement of liquids and gases through pipes and equipment. Measuring how much fluid is flowing is essential for process control and safety. Rotameters are commonly used flow measuring devices in laboratories and industries. This question tests whether you know what basic quantity a rotameter measures in fluid systems.

Given Data / Assumptions:

• The instrument named is a rotameter.
• It is used in piping systems with fluids flowing through them.
• Options mention vortex flow, density of fluids, velocity of fluid in pipes and flow of fluids.
• We assume standard industrial and laboratory usage of a rotameter.

Concept / Approach:
A rotameter is a variable area flowmeter consisting of a tapered vertical tube and a float. Fluid flows upward through the tube and lifts the float until the upward drag force balances the weight of the float. The height of the float is then related to the volumetric flow rate of the fluid. Rotameters are typically calibrated in units of volume per unit time, such as litres per minute. Therefore, they are used to measure the flow rate of fluids, not directly density, velocity or vortex characteristics.

Step-by-Step Solution:
Step 1: Visualise a rotameter as a transparent tapered tube mounted vertically with a float inside. Step 2: When fluid flows upward through the tube, it pushes the float up until forces reach equilibrium. Step 3: The position of the float depends on the flow rate of the fluid, because a higher flow produces a greater drag force. Step 4: The tube is marked with a scale so that the height of the float can be read directly in flow rate units. Step 5: This shows that the primary function of a rotameter is to measure the rate of flow of a fluid, often volumetric flow. Step 6: Although fluid density and viscosity affect calibration, the instrument is not used primarily as a densitometer. Step 7: Therefore, among the options given, flow of fluids is the correct quantity measured by a rotameter.

Verification / Alternative check:
Instrumentation handbooks and process control manuals usually classify rotameters under variable area flowmeters. Their technical specifications focus on flow ranges in volume per unit time and on allowable fluid properties. Other instruments are used to measure density (densitometers), velocity (pitot tubes, ultrasonic meters) or vortex behaviour (vortex shedding flowmeters). In common industrial practice, a rotameter is always associated with measuring the volumetric flow rate, confirming that it is a flow measuring device.

Why Other Options Are Wrong:
Vortex flow refers to flow with vortices and is measured by vortex flowmeters, not by rotameters. Density of fluids is measured by densitometers, hydrometers or other devices, not typically by rotameters. Velocity of fluid in pipes is usually determined by pitot tubes, electromagnetic or ultrasonic flowmeters, rather than by rotameters, which measure overall flow rate.

Common Pitfalls:
Because flow rate is related to velocity and pipe cross sectional area, some learners may think of a rotameter as a velocity meter. While it is true that velocity influences the float position, the instrument is calibrated to show volumetric flow rate rather than local velocity. Remembering the phrase variable area flowmeter for a rotameter can help you connect it directly with flow measurement instead of velocity or density measurement.

Final Answer:
A rotameter is used to measure the flow of fluids, typically as a volumetric flow rate.