Problem:
There are two holes, one on each opposite side of a wide rectangular tank. The cross-section of each hole is 0.01 m², and the vertical distance between the holes is 1 m. The tank is filled with water. What is the net force on the tank in Newton when the water flows out of the holes?

Solution:
To find the net force on the tank, we need to consider the force exerted by the water as it flows out of the holes. This force is a result of the change in momentum of the water.

Step 1: Calculate the mass flow rate:
The mass flow rate can be calculated by multiplying the density of water and the volume flow rate. Since the area of each hole is 0.01 m², the total area of both holes is 0.02 m².

The volume flow rate can be calculated using the equation: Volume flow rate = Area × Velocity.
Assuming the velocity of water flowing out of the holes is the same, let's denote it as v.

The volume flow rate is given by: Volume flow rate = 0.02 m² × v.

Since the density of water is 1000 kg/m³, the mass flow rate is calculated as: Mass flow rate = Volume flow rate × Density = 0.02 m² × v × 1000 kg/m³.

Step 2: Calculate the change in momentum:
The change in momentum can be calculated by multiplying the mass flow rate by the change in velocity.

Initially, the water in the tank is at rest, so the initial velocity is 0. When the water flows out of the holes, it gains a velocity v.

Therefore, the change in momentum is: Change in momentum = Mass flow rate × Change in velocity = 0.02 m² × v × 1000 kg/m³ × v.

Step 3: Calculate the net force:
The net force can be calculated using Newton's second law, which states that force is equal to the rate of change of momentum.

Force = Change in momentum / Time taken.

Since the force is perpendicular to the direction of motion, we can assume it acts horizontally.

The time taken for the water to flow out of the holes can be calculated by considering the vertical distance between the holes and the acceleration due to gravity.

Using the equation: Time = √(2h/g), where h is the vertical distance and g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the values, we get: Time = √(2 × 1 m / 9.8 m/s²).

Now, we can calculate the net force: Force = Change in momentum / Time.

Substituting the values, we have: Force = (0.02 m² × v × 1000 kg/m³ × v) / (√(2 × 1 m / 9.8 m/s²)).

Simplifying the equation will give us the net force on the tank in Newtons.

200 N