The inner cross-sectional area of a pipe decreases from A1 to A2 to A3. Assume the fluid flowing through the pipe is water, and that you can neglect viscosity. At A1, assume you measure a fluid velocity of 0.20 m/s and a gauge pressure of 1 kPa. Assume A2=(1/2)A1 and A3=(1/5)A1. Calculate the gauge pressures at positions A2 and A3.
I'm having trouble finding an equation or a set of equations that can be used to relate the missing variables with the known ones, especially without an actual value for A1. Any help, even just a starting set of equations, would be greatly appreciated!
I'm having trouble finding an equation or a set of equations that can be used to relate the missing variables with the known ones, especially without an actual value for A1. Any help, even just a starting set of equations, would be greatly appreciated!
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Use bernoulli's equation, which in this case says that the pressures divided by specific weight plus one half velocity squared is equal at all points. The velocities can be determined relative to each other because the volume flow rate is constant. (Q = VA). Bernoulli's equation includes a variable z which in this case can just be omitted because the question implores that there is no change in elevation.
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In any flowing liquid, the sum of the pressure head and velocity head remains constant.
So as the velocity head increases in the smaller diameter pipes the pressure head must decrease by the same amount.
Velocity head = Hv = V^2/2g
So as the velocity head increases in the smaller diameter pipes the pressure head must decrease by the same amount.
Velocity head = Hv = V^2/2g