Quasi Steady FLOW - Lecture notes 52 PDF

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QUASI STEADY FLOW Quasi steady flow occurs when we have the fluid head that is causing the fluid to flow is either decreasing or increasing with time. A situation like this occurs when filling or emptying small tanks. For very large reservoirs the fluid head is assumed to be constant.

3.1

TANK EMPTYING THROUGH ORIFICE

A small cylindirical tank of inside diameter coefficient

Example 1

and discharge

in its bottom, is originally full of a liquid of density . To find the time it takes for the

fluid level to drop from a height of that after

with an orifice of diameter

to a height

as shown in the diagram below we may say

second the level in the tank goes down by ℎ metres.

Example 2

3.2 TANK EMPTYING THROUGH PIPE

3.2.2

Flow from one tank to another through a pipe

Example 3 Two water tanks A and B, whose constant cross-sectional areas are 7.4 m2 and 3.7 m2 respectively, are connected by a 50 mm diameter pipe, 120 m long for which the friction coefficient t = w. wN. The initial difference of level between the two tanks is 1.5 m. Find the time taken for 2.25 m3 of water to pass from tank A into tank B if: (a) Pipe entry and exit losses are neglected, (b) If pipe entry and exit losses are taken into account.

(

− MHN H⁄ Q

LMNN H⁄

Example 4

3.3

RESERVOIR EMPTYING OVER WEIR

The same procedure as above is used to find the time T i.e to establish an expression for Q then substitute in equation (3.1) and then integrate between the limits and to obtain T. If for a rectangular weir (or notch) = 1.84Uℎ ⁄ , (Francis formula) following the procedure above T will be found to be H%

N

N

G = N. qsu MN H⁄− MNN H⁄ H

3.4 RESERVOIR WITH SLOPING SIDES Procedure same as above a worked example will be used to demonstrate the concepts involved.

3.5

TIME TO FILL A TANK

Example 5

A circular tank, 1.8 m in diameter and open to the atmosphere at the top, is supplied through a horizontal pipe 30 m long and 50 mm in diameter entering the base of the tank. A pump feeds the pipe and maintains a constant gauge pressue of 45 kN/m2 at the entry to the pipe. Find the time required to raise the level of water in the tank from 0.9 m to 1.8 m above the pipe inlet.

C

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