Fluid Jet Discharge and Vena Contracta
To solve this problem, we need to understand the concept of fluid jet discharge and the formation of the vena contracta.

When a fluid jet discharges from a nozzle, it undergoes a contraction as it leaves the nozzle and enters the surrounding medium. This contraction is known as the vena contracta. The vena contracta is characterized by a reduced diameter compared to the nozzle diameter.

Coefficient of Velocity
The coefficient of velocity (Cv) is a dimensionless quantity that relates the actual velocity at the vena contracta to the theoretical velocity of the fluid jet. It is defined as:

Cv = Actual velocity at vena contracta / Theoretical velocity of the fluid jet

In this problem, the coefficient of velocity is given as 0.95, which means that the actual velocity at the vena contracta is 0.95 times the theoretical velocity of the fluid jet.

Coefficient of Discharge
The coefficient of discharge (Cd) is a dimensionless quantity that relates the actual discharge of the fluid jet to the theoretical discharge based on the nozzle diameter. It is defined as:

Cd = Actual discharge / Theoretical discharge

To find the coefficient of discharge, we need to relate the actual velocity at the vena contracta to the theoretical velocity based on the nozzle diameter.

Relationship between Velocity and Discharge
The relationship between velocity and discharge can be expressed as:

Q = A * V

where Q is the discharge, A is the cross-sectional area, and V is the velocity of the fluid.

At the nozzle exit, the cross-sectional area is given by:

A1 = π * (d1/2)^2

where d1 is the nozzle diameter.

At the vena contracta, the cross-sectional area is given by:

A2 = π * (d2/2)^2

where d2 is the vena contracta diameter.

Calculation of Coefficient of Discharge
The theoretical discharge based on the nozzle diameter is given by:

Q1 = A1 * V1

where V1 is the theoretical velocity at the nozzle exit.

The actual discharge is given by:

Q2 = A2 * V2

where V2 is the actual velocity at the vena contracta.

From the given information, we know that V2 = Cv * V1.

Substituting the values of A1, A2, V1, and V2 into the equations for Q1 and Q2, we can write:

Q1 = π * (d1/2)^2 * V1
Q2 = π * (d2/2)^2 * (Cv * V1)

The coefficient of discharge can then be calculated as:

Cd = Q2 / Q1
= (π * (d2/2)^2 * (Cv * V1)) / (π * (d1/2)^2 * V1)
= (d2/2)^2 * (Cv * V1) / ((d1/2)^2 * V1)
= (d2/2)^2 * Cv / (d1/2)^2

Given that d1 = 100 mm and d2 = 90 mm, we can substitute these values into the equation to find