The fluid jet discharging from a 2" diameter orifice has a diameter of 1.75" at its vena-contracta. The co-efficient of contraction is

The coefficient of contraction (
𝐶
𝑐
C
c
​
) is defined as the ratio of the area of the jet at the vena-contracta to the area of the orifice.

Given:

Diameter of the orifice (
𝐷
1
D
1
​
) = 2 inches
Diameter of the jet at the vena-contracta (
𝐷
2
D
2
​
) = 1.75 inches
First, we need to calculate the areas of the orifice and the jet at the vena-contracta.

The area of a circle is given by:
𝐴
=
𝜋
(
𝐷
2
)
2
A=π(
2
D
​
)
2


So, the area of the orifice (
𝐴
1
A
1
​
) is:
𝐴
1
=
𝜋
(
𝐷
1
2
)
2
=
𝜋
(
2
2
)
2
=
𝜋
(
1
)
2
=
𝜋
A
1
​
=π(
2
D
1
​

​
)
2
=π(
2
2
​
)
2
=π(1)
2
=π

The area of the jet at the vena-contracta (
𝐴
2
A
2
​
) is:
𝐴
2
=
𝜋
(
𝐷
2
2
)
2
=
𝜋
(
1.75
2
)
2
=
𝜋
(
0.875
)
2
=
𝜋
(
0.765625
)
A
2
​
=π(
2
D
2
​

​
)
2
=π(
2
1.75
​
)
2
=π(0.875)
2
=π(0.765625)

Next, the coefficient of contraction (
𝐶
𝑐
C
c
​
) is the ratio of
𝐴
2
A
2
​
to
𝐴
1
A
1
​
:
𝐶
𝑐
=
𝐴
2
𝐴
1
=
𝜋
(
0.765625
)
𝜋
=
0.765625
C
c
​
=
A
1
​

A
2
​

​
=
π
π(0.765625)
​
=0.765625

Therefore, the coefficient of contraction is:
𝐶
𝑐
=
0.765625
C
c
​
=0.765625