Flow through Measurements
1) Derive the expression for rate of flow through venturimeter
2) Derive an expression for the actual discharge through orifice
3) What is a pitot tube? How it is pitot tube used for i)open channel flow ii) pipe flow.
Obtain expression for the same
4) PT the discharge through a triangular notch or weir is given by
8
𝑄 = 15 𝑐𝑑 ×
tan
2
𝛩
× √ 2𝑔 𝐻
3/2
Flow Through Pipes
5) Derive an expression for the head loss in a round pipe of length 1 and coefficient of
friction f. Use the usual notations. Hence obtain Chezy’s equation(Derive the dareyweisbach equation for the loss of head due to friction in a pipe)
6) What are minor losses? List the minor losses and write expressions for each.
7) Define Reynold’s number. What is its significance?
Numerical
8) A horizontal venturimeter with inlet diameter 20 cm and throat diameter 10 cm is used to
measure the flow of oil sp gr 0.8. the discharge of oil through venturimeter is 60 ltr/s.find
the reading of the oil-mercury differential manometer. take cd= 0.98
9) A horizontal venturimeter with inlet diameter 20 cm and throat diameter 10 cm is used to
measure the flow of water. The pressure at inlet is 17.658 N/cm2 and the vacuum
pressure at the throat is 30 cm of mercury. Find the discharge of water through
venturimeter.take cd= 0.98.
10) The inlet and the throat diameters of a horizontal venturimeter are 30 cm and 10 cm
respectively. the liquid flowing through the meter is water. the pressure intensity at inlet
is 13.734 n/cm2 while the vacuum pressure head at the throat is 37 cm of Hg. Find the
rate of flow. Assume that 4% of the differential head is lost between the inlet and throat
.Find also the value of cd for the venturimeter
11) A venturimeter is used for measurement of discharge of water in a horizontal pipeline. if
the ratio of upstream pipe diameter of that throat is 2:1 upstream diameter is 0.3m,the
difference of pressure between throat and upstream is equal to 3 m head of water and loss
of head through is one eight of the throat velocity head, calculate discharge in the pipe
12) In a vertical pipe conveying oil of specific gravity 0.8. two pressure gauges have been
installed at A and B where the diametres are 16 cm and 8 cm respectively. A is 2 metres
above B. The pressure gauge readings have shown that the pressure at B is greater than at
A by 0.981 N/cm2. Neglecting all losses. Calculate the flow rate. if the gauges at A and B
are replaced by tubes filled with the same liquid and connected to a U-tube containing
mercury, calculate the difference of level of mercury in the two limbs of the U-tube
13) Find the discharge of water flowing through a pipe 30 cm diameter placed in an inclined
position where a venturimeter is inserted, having a throat diameter of 15 cm. The
difference of pressure between the main and throat is measured by a liquid of sp. gr. 0.6
in an inverted U-tube which gives a reading of 30 cm. The loss of head between the maul
and throat is 0.2 times the kinetic head of the pipe.
14) A venturimeter is to be installed in a 180mm pipe horizontally at a section where the
pressure is 110 kPa (gauge). If the maximum flow rate of water in the pipe is 0.15m3/s,
find the least diameter of the throat so the pressure at the throat does not fall below 80
kPa (vacuum). Assume that 4% of the differential head is lost between inlet and the
throat.
15) Water is to be supplied to a town of 4 lakhs inhabitants. The reservoir is 6.4 km away
from the town and the loss of head due to friction is measured 15m. Calculate the size of
the supply main if each inhabitant consumes 180 litres of water per day and half of the
daily supply is pumped is 8 hour. Take the coefficient of friction for . f =0.0075.
16) A venturimeter is to be placed in a vertical line to measure the rate of flow of benzene(S
= 0.899). The inlet diameter of venturimeter is 200mm and the throat diameter is 87.5
mm. benzene-Hg differential gauge is used to measure the difference of pressure between
the inlet and the throat of the meter. When the gauge reading is 100 mm. find: (i)gauge
reading in mm of benzene (ii) velocity at throat and discharge. Take Cd = 0.98 and for
mercury sp. gr. = 13.55.
17) A pitot tube is inserted ina pipe of 300 mm diameter.the static pressure in pipe is 100 mm
of Hg.the stagnation pressure at the centre of the pipe ,recorded by the pitot=tube is 0.981
n/cm2. Calculate the rate of flow of water through pipe,if the mean velocity of flow is
0.85 times the central velocity. Take cv=0.98