Fluid Flow Measurement, Viscosity, Buoyancy & Drag

Posted on Mar 2, 2026 in Electromechanical Engineering

Flow Measurement: Pitot and Prandtl Tubes

Explain and describe the basic methods of flow measurement: Pitot tube and Prandtl tube:

Pitot tube: Measures the total (stagnation) pressure at a point.

Prandtl tube: Combines total and static pressure measurements to calculate the local velocity of the fluid using Bernoulli’s equation.

Obstruction Meters and Discharge Methods

Obstruction meters (flow meters): These work by creating a pressure drop by narrowing the passage of the fluid. The main ones are the Venturi, the Nozzle, and the Orifice. The pressure difference allows the volumetric flow rate (Q) to be calculated.

Primary Restriction Devices

  • Venturi: A converging–throat–diverging section that produces a pressure drop with low permanent loss; typically the most efficient.
  • Nozzle: A gradual narrowing that accelerates the fluid; intermediate energy loss.
  • Orifice plate: The simplest restriction device, but with the greatest permanent pressure loss.

Discharge Methods (Tanks)

Torricelli’s theorem: Measures the outlet velocity of a fluid through an orifice. For a fluid under gravity, the ideal exit velocity is v = sqrt(2gh).

Weirs: Used in open channels; the flow rate is determined by measuring the height of the fluid passing over a rectangular obstruction (the weir crest).

Volumetric Flow vs. Mass Flow

Volumetric flow (Q): Volume per unit time (m3/s).

Mass flow (ṁ): Mass per unit time (kg/s), mainly used for gases and other compressible fluids where density varies.

Viscosity and Newton’s Hypothesis

What is viscosity of the fluid? Viscosity is the internal resistance of a fluid to flow or deform when a tangential force (shear stress) is applied. An ideal fluid has no viscosity. A real fluid presents resistance and generates internal friction.

Newton’s hypothesis: States that shear stress (τ) is directly proportional to the rate of deformation (velocity gradient). For a Newtonian fluid, τ = μ (du/dy), where μ is the dynamic viscosity.

Cavitation: Definition and Causes

What is cavitation and when does it occur? Cavitation is the formation of vapor bubbles in a liquid when local pressure drops below the liquid’s vapor pressure. It commonly occurs when the fluid accelerates rapidly (per Bernoulli’s principle), causing a drastic local drop in pressure that reaches or falls below vapor pressure.

Archimedes’ Principle and Floating Conditions

Explain Archimedes’ principle. Any body submerged in a fluid receives an upward thrust (buoyant force) equal to the weight of the fluid it displaces.

Comparison between the object’s weight (W) and the buoyant force (FB):

  • It sinks: The object is heavier than the buoyant force (W > FB). Its density is greater than that of the fluid.
  • Submerged (equilibrium): Weight equals buoyant force (W = FB). The object can remain fully submerged in any position when densities are equal.
  • Floats: The weight equals the buoyant force, but only part of the object is underwater. Its average density is less than that of the fluid.

Types of Forces Acting on Fluids

What types of forces can act on fluid?

  • Surface forces: Act at the boundary of a fluid volume through direct contact (pressure and viscous stresses).
  • Body forces: Act on the entire mass of the fluid without physical contact (e.g., gravity, electromagnetic forces).

Basic Flow Measurement Devices and Principles

Describe basic flow measurement devices and their working principles:

Prandtl / Pitot tube: Uses Bernoulli’s equation. Measures the difference between total and static pressure to obtain the fluid velocity at a given point.

Restriction meters (flow meters): Create a pressure drop by reducing the flow area. Devices include:

  • Venturi: The most efficient with low energy loss.
  • Nozzle: Gradual narrowing; moderate losses.
  • Orifice plate: The simplest, but with the greatest pressure loss.

Weirs: Obstructions in open channels. The flow rate is calculated by measuring the height of the water above the edge of the weir.

Volumetric method: Direct measurement: time the filling of a tank of known volume. This is the most accurate method for calibration.

Sources of Drag and Reduction Methods

Explain basic sources of drag force and methods of its reduction:

Sources of drag:

  • Surface friction (skin friction): Caused by fluid viscosity and friction against the surface of the body; typically greater for elongated bodies.
  • Pressure drag (form or shape drag): Caused by the pressure difference between the front (high) and rear (low) of a body, mainly due to flow separation and wake formation.

Reduction methods:

  • Aerodynamic streamlining: Give the body a teardrop shape to delay flow separation and reduce the low-pressure wake.
  • Surface polishing: Reduce roughness to minimize surface friction.
  • Boundary layer control: Use designs that keep the flow attached to the body for as long as possible (e.g., vortex generators, suction, or blowing).