# Fluid Flow in a Duct of Varying Cross-Section Report

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City University London Fluid Flow in a Duct of Varying Cross-Section Report: Khurshidanjum Pathan, Group A1a Abstract: The experiment is carried out to demonstrate the relation between pressure and fluid velocity in a duct of varying cross-section by using Bernoulli’s equation and continuity equation.(1) Bernoulli’s equation relates the pressure to the velocity for a fluid of constant density flowing in a Venturi tube. Static head, normalised head and percentage of errors were calculated using the result of the data. On the base of calculation its being analysed that in the contraction flow, velocity and dynamic head increases with decreased static pressure and dynamic pressure. While in the convergent flow, velocity decreases with…show more content…
Theory: The continuity equation states the idea that fluid must remain continuous and necessary for the conversation of mass. The continuity equation for incompressible flow with gas or liquid at low velocity is: Av = Q =constant (1) Where, A = Cross-Sectional Area, v = Mean Velocity, Q = Volumetric Flow Rate (1) The Bernoulli’s equation is a momentum based force relation and was derived from the following assumptions: ➢ Steady Flow ➢ Incompressible Flow ➢ Frictionless Flow ➢ Flow along a single streamline Then, the following equation was derived: [pic] (2) Where, p = Static Pressure in[pic], v = Fluid Velocity in m/s, ᵨ = Density of the flowing fluid in [pic] g = acceleration due to gravity in[pic], z = elevation head, constant = total head in m According to Bernoulli’s equation the sum of the three equations is a constant. [pic] = Pressure head = h [pic] = Velocity head Z = Elevation head However, in the experiment the duct is horizontal so, no gravitational force is being applied there. Therefore gz term is being