Calculating Pressure Change in Pipe Flow

Principle of Continuity

The principle of continuity states that the volume flow rate of an incompressible fluid remains constant.

In the larger pipe, the cross-sectional area is 25cm2 and the velocity is 3m/s. So, the volume flow rate is (25cm2) * (3m/s) = 75 cm3/s.

In the smaller pipe, the cross-sectional area is 15cm2. By rearranging the equation for velocity as volume flow rate divided by cross-sectional area, we find the velocity in the smaller pipe to be 5 cm/s.

Bernoulli's Equation

Bernoulli's equation states that the sum of the pressure, potential energy, and kinetic energy per unit volume of an incompressible, non-viscous fluid remains constant along a streamline.

As the cross-sectional area decreases and velocity increases, we can calculate the pressure change by using the equation:

(pressure at smaller pipe) - (pressure at larger pipe) = 0.5 * (density of water) * ((velocity in larger pipe)^2 - (velocity in smaller pipe)^2)

Assuming the density of water is 1000 kg/m3, we calculate the pressure change as:

(pressure at smaller pipe) - (pressure at larger pipe) = 0.5 * (1000 kg/m3) * ((3 m/s)^2 - (5 cm/s)^2)

Converting the units and calculating further, we find the pressure change to be 4498.75 Pascal (Pa) or 4498.75 N/m2.

Therefore, the pressure change that occurs on going from the larger diameter pipe to the smaller pipe is 4498.75 Pascal (Pa).