A liquid of density 1170 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.75 m/s and the pipe diameter d1 is 11.7 cm. At Location 2, the pipe diameter d2 is 16.3 cm. At Location 1, the pipe is Δy=8.87 m higher than it is at Location 2. Ignoring viscosity, calculate the difference ΔP between the fluid pressure at Location 2 and the fluid pressure at Location 1.
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
A liquid of density 1170 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.75 m/s and the pipe diameter d1 is 11.7 cm. At Location 2, the pipe diameter d2 is 16.3 cm. At Location 1, the pipe is Δy=8.87 m higher than it is at Location 2. Ignoring viscosity, calculate the difference ΔP between the fluid pressure at Location 2 and the fluid pressure at Location 1.
According to equation of continuity, flow rate of fluid remains constant at every point in a pipe.
hence,
Bernoulli's equation for pressure difference is as follows:
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