Water flows through a pipe of 100 mm at the rate of 0.9 m3 per minute at section a. it tapers to 50mm diameter at b, a being 1.5 m above b. the pressure in the pipe at a is 70 kpa above atmospheric. assuming no loss of energy between a and b, determine, a)- the velocity of a and b b)- find pressure at b

The velocities in points A and B are 1.9 and 7.63 m/s respectively. The Pressure at point B is 28 Kpa.

Explanation:

Assuming the fluid to be incompressible we can apply for the continuity equation for fluids:

Where A, V and Q are the areas, velocities and volume rate respectively. For section A and B the areas are:

Using the volume rate:

Assuming no losses, the energy equation for fluids can be written as:

Here P, V, p, z and g represent the pressure, velocities, height and gravity acceleration. Considering the zero height level at point A and solving for Pb:

Knowing the manometric pressure in point A of 70kPa, the height at point B of 1.5 meters, the density of water of 1000 kg/m^3 and the velocities calculated, the pressure at B results:

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