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Diploma in Civil Engineering

PREPARED BY : NORINI BINTI SHAMSUDIN CIVIL ENGINEERING DEPARTMENT

Diploma in Civil Engineering

Apply appropriate fluid concept to determine parameters that act in hydrostatic device and act on immersed surface

At the end of this chapter, student should be able to:

 Define velocity and flow rate

 State Continuity equation  Calculate the velocity and flow rate using Continuity equation

for a. tapered pipe b. branched pipe

At the end of this chapter, student should be able to:

 Apply Bernoulli’s equation , its application and relationship to

following parameters a. Relate pressure energy, kinetic energy and potential

energy in terms of head b. Principle of conservation of energy c. Calculate flow rate through: i.

Uniform pipe

ii. Tapered pipe iii. Venturi meter iv. Small and large orifice

DEFINE VELOCITY AND FLOW RATE Diploma in Civil Engineering

 The average speed of an object is defined as the distance traveled divided by the time elapsed.  It is generally denoted by v.  Unit = m/s

𝑠 v= 𝑡

s = distance travel t = time

DEFINE VELOCITY AND FLOW RATE Diploma in Civil Engineering

The quantity of a liquid, flowing per second through a section of a pipe or a channel. Also known as rate of discharge or simply discharge. It is generally denoted by Q. Unit = m3/s

Q = Av

A = Cross-sectional area of the pipe v = velocity of the liquid

STATE CONTINUITY EQUATION Diploma in Civil Engineering

If an incompressible liquid is continuously flowing through a pipe or a channel (whose cross-sectional area my or may not be constant) the quantity of liquid passing per second is the same at all section

Figure 6.1. Continuity of a liquid flow

𝑄1 = 𝑄2 = 𝑄2

CALCULATE THE VELOCITY AND FLOW RATE USING CONTINUITY EQUATION Diploma in Civil Engineering

Water is flowing through a uniformly tapered pipe having end diameters of 150mm and 50mm respectively. Find the discharge at the larger end and velocity at the smaller end, if the velocity of water at the larger end is 2m/s

CALCULATE THE VELOCITY AND FLOW RATE USING CONTINUITY EQUATION Diploma in Civil Engineering

Water is flowing through a pipe of 100 mm diameter with an average velocity of 10 m/s. Determine the rate of discharge of the water. Also determined the velocity of water at the other end of the pipe, if the diameter of the pipe is gradually changed to 200 mm

CALCULATE THE VELOCITY AND FLOW RATE USING CONTINUITY EQUATION Diploma in Civil Engineering

Figure 6.2

A pipe AB branches into two pipes C and D as shown in figure 3.2. The pipe has diameter of 0.45m at A, 0.3m at B, 0.2m at C and 0.15m at D. Find the discharge at A, if the velocity of water at A is 2 m/s. Also find out the velocities at B and D, if velocity at C is 4 m/s.

Diploma in Civil Engineering

EXERCISE 6.1 1. The water is flowing through a pipe line of 100 mm diameter with a velocity of 1.5 m/s. Determine the discharge through the pipe. [Ans. 0.0118 m3/s] 2. Find the size of pipe, which has to discharge an oil, at the rate of 2 m3/s and of specific gravity 0.8 with a velocity of 3 m/s . [Ans. 0.92m] 3. What is the flow rate of water in l/s for a 0.2m diameter pipe, if the average velocity of flow is 1.5m/s. if the pipe reduces to 0.1m din diameter at another section. What is the velocity of flow at that section? [Ans. 47.1 l/s; 6 m/s]

Diploma in Civil Engineering

4. Water runs through a water main of cross-sectional area 0.4 m2 with a velocity of 6 m/s. Calculate the velocity of the water in the pipe when the pipe tapers down to a cross-sectional area of 0.3 m2. [Ans. 8 m/s] 5. Water enters a typical garden hose of diameter 1.6 cm with a velocity of 3 m/s. Calculate the exit velocity of water from the garden hose when a nozzle of diameter 0.5 cm is attached to the end of the hose. [Ans. 30.6 m/s]

Diploma in Civil Engineering

6. A water tank has 3cm diameter at inlet A, 4cm diameter outlet at B and 3cm diameter controllable inlet at C (Figure 6.3). if the velocity of water at the inlet A is 2 m/s and the velocity of flow going out at B is 1.85 m/s. Calculate the velocity at the inlet C? [Ans: 1.85 m/s] 7. A pipe 0.6m in diameter branches into two pipes of diameters 0.4m and 0.3m (Figure 6.4). The average velocity in main pipe is 4.5 m/s. Determine the velocity in the 0.3m diameter pipe if the average velocity in the 0.4m diameter pipe is 3.5m/s. [Ans: 11.88 m/s]

Figure 6.3

Figure 6.4

8.

9.

A pipe PQ branches into two pipes R and S shown in Figure 6.5. The pipe has diameter 400mm at P, 300m at Q; 250mm at R and 200mm at S. Determine the discharge at P if the velocity at P is 2m/s. Also determine the velocities at Q and R, if the velocity at S is 4m/s [Ans: 0.25 m3/s; 2.86m/s; 2.48m/s]

Water flows through a pipe PQ 1200mm diameter and 3.5m/s and the passes through a pipe QR 1500mm diameter. At R, the pipe branches. Branch RS is 800mm in diameter 1 and carries of the flow in PQ. The flow 4 velocity in branch RT is 3m/s. Calculate the rate of flow in PQ, the velocity in QR, the velocity in RS and the diameter of RT. [Ans: 3.96m3/s; 2.24m/s; 1.97m/s; 1.12m]

Figure 6.5

Figure 6.6

BERNOULLI’S EQUATION

Diploma in Civil Engineering

•

•

Bernoulli’s theorem states that ‘for a perfect incompressible stream, the total energy of a particle remains the same, while the particle moves from one point to another. It is assume that there are no losses due to friction in the pipe. 𝑣2 𝑃

𝑍+

2𝑔

+

𝜌𝑔

= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

𝑍 = 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦

Where,

𝑣2 = 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐸𝑛𝑒𝑟𝑔𝑦 2𝑔 𝑃 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐸𝑛𝑒𝑟𝑔𝑦 𝜌𝑔

BERNOULLI’S EQUATION

Diploma in Civil Engineering

The Bernoulli’s equation as expresses above can be applied between any two points, 1 and 2 (or 2 and 3 or 1 and 3) as shown in Figure 6.7 in a steady flow of an incompressible fluid as

𝑣12 𝑃1 𝑣22 𝑃2 𝑧1 + + = 𝑧2 + + 2𝑔 𝜌𝑔 2𝑔 𝜌𝑔

Figure 6.7

BERNOULLI’S EQUATION

Diploma in Civil Engineering

𝑧 = 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑤𝑒𝑖𝑔ℎ𝑡 𝑖𝑠 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 ℎ𝑒𝑎𝑑 𝑣2 = 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 𝑤𝑒𝑖𝑔ℎ𝑡 𝑖𝑠 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 ℎ𝑒𝑎𝑑 2𝑔 𝑃 = 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 per unit weight is known as pressure head 𝜌𝑔

Diploma in Civil Engineering

 States that the total amount of energy within an isolated system is constant.  Although energy can be transformed from one form into another, energy cannot be created or destroyed. 𝐸𝑖𝑛 − 𝐸𝑜𝑢𝑡

𝑑𝐸𝑐𝑣 = 𝑑𝑡

Where 𝐸𝑖𝑛 and 𝐸𝑜𝑢𝑡 are the total rate of energy transfer into 𝑑𝐸 and out of the control volume, and 𝑐𝑣 is the rate of change 𝑑𝑡 of energy within the control volume.

Diploma in Civil Engineering

A pipe is 50mm in diameter and pressure is 200kN/m2 with an average velocity of 2m/s. Plumbing is at level of 9m from datum. Calculate the total energy when water flows through pipe.

Diploma in Civil Engineering

Figure 6.8

The diameter of a pipe changes from 200 mm at a section 5 meters above datum to 50 mm at section 3 meters above datum (Figure 6.8). The pressure of water at first section is 500kPa. If the velocity of flow at the first section is 1 m/s, determine the intensity of pressure at the second section.

Diploma in Civil Engineering

Figure 6.9

A pipe 300 meters long has a slope 1 in 100 and tapers from 1 meter diameter at the higher end to 0.5 meter at the lower end. The quantity of water flowing is 900 liters/second. If the pressure the higher end is 70kPa, find the pressure at the lower end

EXERCISE 6.2 Diploma in Civil Engineering CC303 Hydraulics I 1. A uniformly tapering pipe has a 120mm and 80mm diameters at its ends. If the velocity of water at the larger end is 2m/s, find the discharge at the larger end and the velocity head at the smaller. [Ans. 22.62 liters/s ; 1.03m] 2. Find the total head of water flowing with the velocity of 8 m/s under a pressure 80kPa. The center line of the pipe is 5m above the datum line. [Ans. 16.41m] 3.

A horizontal pipe 100m long uniformly tapers from 300mm diameter to 200mm diameter. What is the pressure at the smaller end, if the pressure at the larger end is 100kPa and the pipe is discharging 50 liters of water per second. [Ans. 99.1kPa]

Diploma in Civil Engineering

CC303 Hydraulics I

4. A pipe 5 meter long is inclined at angle of 15o with the horizontal. The smaller section of the pipe, which is at lower level, is of 80 mm diameter and the larger section of the pipe is 240 mm diameter as shown in Figure 6.10. Determine the difference of pressure between the two sections, if the pipe is uniformly tapering and the velocity of water at the smaller section is 1m/s [Ans. 12.2 kN/m2]

Figure 6.10

Diploma in Civil Engineering

CC303 Hydraulics I

5. Water is flowing through a pipe at the rate 35 liters/s having diameters 200 mm and 100 mm at section 1 and 2 respectively. The section 1 is 4m above the datum and section 2 is 2m above the datum. Find the pressure at section 2 if the pressure at section 1 is 40kPa. [Ans. 50.3kPa] 6. A 200 m long pipe slope down at 1 in 100 and tapers from 0.25m diameter to 0.15m diameter at the lower end. If the pipe carries 100 liters of oil of specific gravity 0.85, find the pressure at the lower end. The upper end gauge reads 50kPa. [Ans. 45.1 kPa]

Diploma in Civil Engineering

Figure 6.11

A venturimeter is an apparatus for finding out the discharge of a liquid flowing in a pipe. Its consist of the following three parts: a) Convergent cone b) Throat c) Divergent cone

Diploma in Civil Engineering

CC303 Hydraulics I

a) Convergent cone It is a short pipe which converges from a diameter 𝑑1 to a smaller diameter 𝑑2 . The convergent cone is also known as inlet of the venturimeter. b) Throat It is a small portion of circular pipe in which the diameter 𝑑2 is kept constant. c) Divergent cone It is a pipe, which diverges from a diameter 𝑑2 to a large diameter 𝑑1 . The divergent cone is also known as outlet of the venturimeter.

Diploma in Civil Engineering

CC303 Hydraulics I

•

The liquid, while flowing through the venturimeter, is accelerated between the section 1 and 2.

•

As a result of acceleration, the velocity of the liquid at section 2 (the throat) become higher than that at section 1.

•

This increase in velocity results in considerably decreasing the pressure at section 2.

•

The liquid, while flowing through the venturimeter, is decelerated between the section 2 and 3. As a result, the velocity of liquid decrease which consequently increase the pressure.

•

Diploma in Civil Engineering

𝑄𝑡ℎ𝑒𝑜𝑟𝑦 =

𝑄𝑎𝑐𝑡𝑢𝑎𝑙 =

𝐴1 𝐴2 𝐴12 − 𝐴22 𝐶𝑑 𝐴1 𝐴2 𝐴12 − 𝐴22

2𝑔𝐻

2𝑔𝐻

𝜌′ − 𝜌 𝑥 H= 𝜌

𝜌′ = 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑛 𝑚𝑎𝑛𝑜𝑚𝑒𝑡𝑒𝑟 𝜌 = 𝑙𝑖𝑞𝑢𝑖𝑑 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑛 𝑝𝑖𝑝𝑒 𝑥 = different of pressure at entrance and throat read by a manometer

Figure 6.12

One ventury meter has a diameter of 76mm and throat of 38mm as shown in Figure 6.12. The pressure difference is measured by mercury manometer. The level of mercury in two different arms of the manometer is 266mm. If the 2200 liters of water flow through the ventury meter in 4 minutes, determine the coefficient of discharge

Diploma in Civil Engineering

𝑄𝑎𝑐𝑡𝑢𝑎𝑙 =

𝐶𝑑 𝐴1 𝐴2 𝐴12 − 𝐴22

2𝑔𝐻

𝐷1 = 0.076 𝑚 𝜋𝐷2 𝜋 × 0.0762 𝐴1 = = = 4.536 × 10−3 𝑚2 4 4 𝐷2 = 0.038 𝑚 𝜋𝐷2 𝜋 × 0.0382 𝐴2 = = = 1.134 × 10−3 𝑚2 4 4

𝑉 2.2𝑚3 𝑄= = = 9.17 × 10−3 𝑚3 /𝑠 𝑡 4 × 60 𝑠

Diploma in Civil Engineering

𝜌′ = 13600 𝑘𝑔/𝑚3 , 𝜌 = 1000 𝑘𝑔/𝑚3 , 𝑥 = 0.266 𝑚 𝜌′ − 𝜌 𝑥 13600 − 1000 0.266 𝐻= = = 3.352 𝜌 1000 𝑄=

𝐶𝑑 𝐴1 𝐴2 𝐴12

−

𝐴22

9.17 × 10−3 =

9.17

× 10−3

𝐶𝑑 = 0.96

2𝑔𝐻 𝐶𝑑 × (4.536 × 10−3 ) × 1.134 × 10−3 4.536 ×

10−3 2

4.171 × 10−5 𝐶𝑑 = 4.392 × 10−3

− 1.134 ×

10−3 2

2 × 9.81 × 3.352

Figure 6.13

One ventury meter has a diameter of 20cm and throat of 12.5cm as shown in Figure 6.13. The pressure difference is measured by mercury manometer. The level of mercury in two different arms of the manometer is 87.8cm. Calculate the discharge at the throat.

Diploma in Civil Engineering

• An opening, in a vessel, through which the liquid flow out is known as an orifice. • The usual purpose of an orifice is the measurement of discharge, • An orifice may be provided in vertical side of a vessel or in the base. • There are many types of orifice depending upon their size; example: small orifice and large orifice

Diploma in Civil Engineering

orifice

orifice

Diploma in Civil Engineering

• Consider a tank, fitted with an orifice, as shown in Figure 6.14 • The liquid particles, in order to flow out through the orifice, move towards the orifice from all direction. • It may be noted, that the liquid particles lose some energy, while taking the turn to enter into the orifice.

Figure 6.14

Diploma in Civil Engineering

• Thus, observed that the jet, after leaving the orifice get contracted. • The maximum contraction takes place at a section slightly on the downstream side of the orifice, where the jet is more or less horizontal. • Such a section is known as vena contracta as shown by the section C-C in Figure 6.14

Figure 6.14

Diploma in Civil Engineering

The ratio of area of the jet at vena contracta to the area of the orifice 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑗𝑒𝑡 𝑎𝑡 𝑣𝑒𝑛𝑎 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑎, 𝐴𝑐 𝐶𝑐 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑜𝑟𝑖𝑓𝑖𝑐𝑒, 𝐴𝑜

The ratio of actual velocity of the jet at vena contracta to the theoretical velocity of the jet 𝐴𝑐𝑡𝑢𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑗𝑒𝑡 𝑎𝑡 𝑣𝑒𝑛𝑎 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑎, 𝑣𝑐 𝐶𝑣 = 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑗𝑒𝑡, 𝑣𝑜

Diploma in Civil Engineering

The ratio of actual discharge through an orifice to the theoretical discharge 𝐴𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 𝐶𝑑 = 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 𝐴𝑐𝑡𝑢𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝐴𝑐𝑡𝑢𝑎𝑙 𝐴𝑟𝑒𝑎 𝐶𝑑 = 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝐴𝑟𝑒𝑎 𝐴𝑐𝑡𝑢𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝐴𝑐𝑡𝑢𝑎𝑙 𝐴𝑟𝑒𝑎 𝐶𝑑 = × 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝐴𝑟𝑒𝑎

𝑪𝒅 = 𝑪𝒗 × 𝑪𝒄

Diploma in Civil Engineering

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑎𝑡 𝑡ℎ𝑒 𝑜𝑟𝑖𝑓𝑖𝑐𝑒, 𝑣 =

2𝑔ℎ

𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑎𝑡 𝑣𝑒𝑛𝑎 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑎, 𝑣 = 𝐶𝑣 2𝑔ℎ

𝑇ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒, 𝑄 = 𝐴 2𝑔ℎ

𝑅𝑒𝑎𝑙 𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒, 𝑄 = 𝐶𝑑 𝐴 2𝑔ℎ

Diploma in Civil Engineering

A jet of water issues from an orifice of diameter 16mm under a constant head 1.5m. Find the coefficient of discharge for the orifice, when the actual discharge is 0.65 litres/s

Diploma in Civil Engineering

𝑄 = 𝐶𝑑 𝐴 2𝑔ℎ 𝐷 = 0.016 𝑚 , 𝑄 = 0.65 × 10−3 𝑚3 /𝑠 𝜋𝐷2 𝜋 × 0.0162 𝐴= = = 2.01 × 10−4 𝑚2 4 4

𝑄 = 𝐶𝑑 𝐴 2𝑔ℎ 0.65 × 10−3 = 𝐶𝑑 × 2.01 × 10−4 2 × 9.81 × 1.5 𝐶𝑑 =

0.65×10−3 1.09×10−3

𝐶𝑑 = 0.60

Diploma in Civil Engineering

A 60 mm diameter orifice is discharging water under a head of 9m. Calculate the real discharge and the velocity at vena contracta, if Cd = 0.625 and Cv = 0.98.

Diploma in Civil Engineering

𝐶𝑣 =

𝑥2 4𝑦ℎ

𝑣=

𝑔𝑥 2 2𝑦

Diploma in Civil Engineering

A jet of water issues from an orifice under a head of 160mm. Determine the coefficient of velocity of the jet, if the horizontal distance travelled by a point on the jet is 320mm and vertical distance is 170mm.

Diploma in Civil Engineering

ℎ = 0.16𝑚 , 𝑥 = 0.32𝑚 , 𝑦 = 0.17𝑚

𝐶𝑣 =

=

𝑥2 4𝑦ℎ 0.322 4×0.32×0.17

= 0.69

Diploma in Civil Engineering

Water of discharge at the rate of 98.2 liters/s through a 120mm diameter vertical sharp edged orifice under a constant head of 10m. A point, on the jet measured from the vena contracta has co-ordinates of 4.5m horizontal and 0.54m vertical. Find the values of Cv, Cc and Cd the orifice.

Diploma in Civil Engineering

𝑄=

3 2 2 𝐶𝑑 𝑏(𝐻2 3

−

3 2 𝐻1 )

Diploma in Civil Engineering

A rectangular orifice of 1.5m wide and 0.5m deep is discharging water from a tank. If the water level in the tank is 3m above the top edge of the orifice, find the discharge through the orifice. Take the coefficient discharge for the orifice as 0.6.

Diploma in Civil Engineering

EXERCISE 6.3 1. A flow passes through an orifice of diameter 25mm under a head of water 1.22 is 1.53 x 10-3 m3/s. Calculate the discharge coefficient. [Ans. 0.63] 2. Find the discharge through a small orifice of 150mm deep and 400mm wide under a constant head of 250mm. Take Cd as 0.625. [Ans. 0.083 m3/s]

Diploma in Civil Engineering

CC303 Hydraulics I

3. A jet of water issues from an orifice under a head of 160mm. Determine the coefficient of velocity of the jet, if the horizontal distance travelled by a point on the jet is 320mm and vertical distance is 170mm. [Ans. 0.63] 4. Find the discharge through a small orifice of 150mm deep and 400mm wide under a constant head of 250mm. Take Cd as 0.625. [Ans. 0.083 m3/s]

Diploma in Civil Engineering

CC303 Hydraulics I

5. In laboratory, 53.5 litres of water per second is collected through a small orifice of 100 mm deep and 250mm wide under a constant head of 600mm. Find the coefficient of discharge. [Ans. 0.622]

6. A large rectangular orifice of 1.2m wide and 0.6m deep is discharging water from a tank, where the level is 0.6m above the upper edge of orifice. Find the discharge through the orifice, is the coefficient of discharge as 0.6. [Ans. 1.83 m3/s]

Diploma in Civil Engineering

CC303 Hydraulics I

7.

A horizontal venturimeter of size 0.5m (inlet) and 0.25 (throat) is used to measured the flow of oil of specific gravity 0.9. The discharge of oil through venturimeter is 100 l/s. Find the reading of mercury differential manometer. Take the coefficient of dicharge as 0.98. [Ans. 0.0146m]

8.

A horizontal venturimeter 20 cm (inlet) and 10 cm (throat) is used to measure the flow of oil of specific gravity 0.7. Determine the difference of mercury manometer reading if the coefficient of discharge as 1.0. [Ans. 2.829 m]

Diploma in Civil Engineering

9. A 40 mm diameter orifice is provided in a tank containing water to a height of 1.2m above the centre of the orifice. The values of Cv and Cc are 0.98 and 0.62. Find: i. Coefficient of discharge, Cd ii. Theoretical discharge iii. Actual discharge [Ans: 0.608; 6.097 l/s ; 3.706 l/s] 10. Water discharge at the rate of 70 l/s through 10 cm diameter vertical sharp-edged orifice placed under a constant head of 9 m. A point on the jet measured from vena contracta of the jet has coordinates 4.5m horizontal and 0.6m vertical. Find the coefficients: [Ans: Cd = 0.67; Cv = 0.968 ; Cc = 0.69]