CHEMICAL ENGINEERING

SECTION 6

Flow and Pressure Measurement

PROBLEM 6.1

Sulphuric acid of density 1300 kg/m^3 is flowing through a pipe of 50 mm internal diam-
eter. A thin-lipped orifice, 10 mm diameter, is fitted in the pipe and the differential pressure
shown by a mercury manometer is 10 cm. Assuming that the leads to the manometer are
filled with the acid, calculate (a) the mass of acid flowing per second, and (b) the approx-
imate loss of pressure caused by the orifice. The coefficient of discharge of the orifice
may be taken as 0.61, the density of mercury as 13,550 kg/m^3 , and the density of water
as 1000 kg/m^3.

Solution

See Volume 1, Example 6.2.

PROBLEM 6.2

The rate of discharge of water from a tank is measured by means of a notch, for which
the flowrate is directly proportional to the height of liquid above the bottom of the notch.
Calculate and plot the profile of the notch if the flowrate is 0.1m^3 /s when the liquid
level is 150 mm above the bottom of the notch.

Solution

The velocity of fluid discharged as a heighthabove the bottom of the notch is:

uD

√

 2 gh

The velocity therefore varies from zero at the bottom of the notch to a maximum value
at the free surface.
For a horizontal element of fluid of width 2wand depth dhat a heighthabove the
bottom of the notch, the discharge rate of fluid is given by:

dQD

√

 2 gh 2 wdh

If the discharge rate is linearly related to the height of the liquid over the notch,H,w
will be a function ofhand it may be supposed that:

wDkhn

wherekis a constant.

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