5) You mark two points on a water pipe which is horizontally positioned with wat

Question

5) You mark two points on a water pipe which is horizontally positioned with water flowing through it from left to right. The diameter of the pipe at the left mark is 3.873 cm and at the right mark is 2.088 cm. What is the pressure difference between left and right (see sheet 29,25) if the velocity of the fluid on the left is 9.579 cm/s ? Now tilt the pipe such that the right mark is higher than the left mark and indicate with a negative (positive) sign whether the pressure difference increases (decreases) for the same given velocity.

Explanation / Answer

Diameter of the pipe at left mark d = 3.873 cm Diameter pf the pipe at right mark D = 2.088 cm Velocity of the fluid at left mark v = 9.579 cm / s Velocity of the fluid at right mark v ' = ? From equation of continuity Av = A' v '                                        d 2 v = D 2 v ' From this v ' = v ( d/ D ) 2                     = 32.95 cm / s Pressure difference P = ( 1/ 2) [ v ' 2 - v 2 ] Since from Bernoulli's theorem Where = density of water                = 1000 kg / m 3 Substitute values we get   P = 497.21 x 10 3 Pa                               = 32.95 cm / s Pressure difference P = ( 1/ 2) [ v ' 2 - v 2 ] Since from Bernoulli's theorem Where = density of water                = 1000 kg / m 3 Substitute values we get   P = 497.21 x 10 3 Pa          

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