Fluid mechanics Assignment Example | Topics and Well Written Essays - 2000 words

Fluid mechanics - Assignment Example Introduction When a fluid undergoes motion, there are certain laws it must satisfy. Two of the basic laws pertain to the conservation laws for mass and energy. While the conservation of mass leads to Continuity Equation, conservation of energy gives us Bernoulli’s Principle. (1) Continuity Equation: the amount of fluid volume per unit time must remain constant as the fluid cannot be compressed (no density variation) and the mass flowing in to a certain area per unit time must always be same to that going out from that area in exactly the same time. Thus, leading to the important equation Q = A1 ? u1 = A2 ? u2 .....(1) where A1 and u1 are the cross-sectional area and fluid velocity respectively at the location ‘1’; and A2 and u2 are those at ‘2’ along the Venturi Tube shown below. (2) Bernoulli’s Equation: similarly, when we take into account the conservation of total energy of the water in the Tube, which happens to be one of the most fundament al conservation principles in Physics, we obtain the Bernoulli’s equation. ... ic Head† or â€Å"Pressure Head†, denoting the energy due to the fluid pressure; the 2nd term defined as â€Å"Velocity Head†, denoting the kinetic energy; and the 3rd term named as â€Å"Potential Head†, denoting potential energy, combine together to give the total energy or â€Å"Head† of the fluid in motion. Apparatus Used (1) Venturi Tube or Venturimeter (2) Stopwatch (3) Graduated Beaker 1 2 3 4 5 6 7 8 9 10 11 Venturimeter or Venturi Tube Methodology Step 1: Known volume of water (10 litres in the first case) is allowed to flow in through the inlet, located at position marked as ‘1’ Step 2: when the water flows through the Venturi Tube and goes out through the valve at ‘11’, it is collected in the graduated beaker and the volume is noted down along with the total time taken to travel through the Tube. Subsequently, Q, the Volumetric Flow Rate is measured using the Eqn. (1) Step 3: simultaneously, the heights of the wat er columns in each of the 11 capillary tubes connected to the Venturimeter at 11 different locations are also observed carefully and put the relevant column in the Observation Table 1 below Step 4: the Velocity Head and Pressure Head as given by Eqn. (2) are also calculated for different fluid velocities at different locations, and the values are tabulated in Columns 6 & 8 respectively Step 5: finally, the total energy or Head of the fluid is measured just by adding the Velocity Head and the Pressure Head since the Potential Head remains unchanged Step 6: all the 5 steps mentioned above are repeated for 20 litres and 25 litres and the measurements are recorded in Tables 2 & 3 Step 7: bar diagrams are plotted for Evh, the Velocity Head, against the Tube Locations. Similarly, another graph is plotted for Esh, the Static Head, Vs the Tube