Fluid Mechanics - Bernoullis Equation - Lab Report Example

When an incompressible fluid starts moving along streamlines, two basic laws get satisfied. One can use these two laws to check the behavior of the dynamics of the fluid. Moreover, both these laws pertain to certain conservation of fluid properties— (1) Continuity Equation: from the consideration of mass conservation one can show that the net volume of fluid per unit time always remains constant as the fluid is incompressible (no variation in density), giving us Q = A1 × v1 = A2 × v2 where Ai and vi are the cross-sectional area and fluid velocity at the ith location. (2) Bernoulli’s Equation: again we have from the consideration of conservation of energy of the fluid, the Bernoulli’s equation P1/ρg + v12/2g + Z1  =  P2/ρg + v22/2g + Z2 + HL  where HL denotes the Head Lost due to fluid resistance, and all other symbols expressing usual meanings.

While the first term is known as Static Head or Pressure Head, the second term is called Velocity Head; and the third term, denoting the Potential Head is zero in our case as the height of the axis at the inlet and outlet is same. In order to verify the basic laws of fluid dynamics, we have used a Venturi Tube or Venturimeter as described in the figure above. The fluid (water in our case) is allowed to flow in through the left-hand-side valve and it goes out through the right-hand-side valve of exactly equal cross-sectional area.

In between these two extreme ends, there exist 9 other locations along the axis of the Tube where capillaries are inserted to measure the Pressure Head of the fluid flow from the height of the water in each tube. Thus, one can measure pressure at 11 different locations along the axis of the Venturimeter which is assumed to be the zero Potential Energy line for the fluid. As soon as the fluid flows through the Tube, the total time taken by it to cross-over the horizontal length of the Tube is also noted using a stopwatch, to calculate the Volumetric Flow Rate after determining the total volume of water collected.

Besides, the height of the water in each of the 11 different capillary tubes is also measured and tabulated in Tables 1-3 below, for 3 different volumes of inflows. We observe here as well that there exists mismatch in the Total Energy. Since the Total Energy at the inflow valve was 0.2793 and that at the outflow valve was 0.2402, the Head Lost due to fluid resistance may be calculated as