Final answer:
To find the speed of the fluid near the right-hand end of the tube, we can use the equation of continuity. Substituting the given values into the equation and solving, we find that the speed of the fluid near the right-hand end of the tube is approximately 6.251 m/s.
Step-by-step explanation:
To calculate the speed of the fluid near the right-hand end of the tube (v2), we can use the equation of continuity. The equation states that the product of the cross-sectional area of a pipe and the speed of the fluid remain constant as long as the density is constant. In this case, the initial cross-sectional area (A1) is given and the cross-sectional area at the right-hand end of the tube (A2) can be calculated using the ratio of the cross-section areas of the pressures (Pi - P2 = dP = 27.5 Pa) and the known density of the fluid (1.27 kg/m^3). Using the equation of continuity, we can set up the following equation: A1 * v1 = A2 * v2, Solving for v2: v2 = (A1 * v1) / A2. Substituting the values and converting the units, we get: v2 = (π * (0.55/2)^2 * 1.8 m/s) / (π * (0.31/2)^2). Simplifying the equation, we find that v2 is approximately 6.251 m/s.