IQuestioWater is draining off from the large and wide reservoir through a long,

Question

IQuestioWater is draining off from the large and wide reservoir through a long, narrow, and straight pipe under a gravity field. The length of the pipe is 40 m and the depth of water in the tank is 5 m., The diameter of the tank is 5 m and the inside diameter of the pipe is 30 cm (density of water- standard gravity-9.81 m/s) (a) Ca steady state, frictionless, turbulent, and incompressible lculate the velocity of draining water at the end of the pipe in SI unit by assuming that the flow is (b) Calculate the velocity again when the flow is laminar and the friction loss is 10 J/kg. Answer: 20.7 ms (In fact, a laminar flow is impossible due to high Re value)

Explanation / Answer

Given Data -

Pipe

Tank

Density of water = 998 kgm-3 , Gravity = 9.8 ms-2

Velocity is calculated as = 29.7 ms-1 (already given)

There are certain assumptions made for the precision of the value for velocity. These assumptions are mainly that the water flow is steady and nature of flow is can be turbulent or laminar depending on the pressure of the system.(First system is frictionless)

Velociity in 2nd case decreases from 29.7 to 20.7 m/s since there is loss of energy due to friction as the friction loss is given of 10 J/Kg.

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