Hi guyys, could you help me with this question.

The center of a circular floodgate of radius 0.5 m is located in a dam at a depth of 2 m beneath the free surface of the water contained by the dam. Calculate the force exerted by the water on the floodgate. The density of water is 977 kg/m3 .

n if possible can u give me a full solution,I need to understand the concept so that i can continue doing the next question. thank you.
Ans: 23050 N

a hemispherical bowl of radius 0.5 m is filled with water of density 997 kg/m^3.

calculated the force exerted by the bowl.

ans: 3840 N

To calculate the force exerted by the water on the floodgate, we need to find the pressure exerted by the water at the depth of the floodgate and then multiply it by the area of the floodgate.

Step 1: Calculate the pressure exerted by the water at the depth of the floodgate.

The pressure exerted by a fluid at a depth can be calculated using the formula:

P = ρ * g * h

Where:
P is the pressure
ρ is the density of the fluid
g is the acceleration due to gravity
h is the depth

Given:
Density of water (ρ) = 977 kg/m³
Depth of the floodgate (h) = 2 m
Acceleration due to gravity (g) = 9.8 m/s²

P = 977 * 9.8 * 2
P = 19132.4 Pa (Pascals)

Step 2: Calculate the force exerted by multiplying the pressure by the area of the floodgate.

The pressure acts uniformly on the entire surface of the floodgate. The area of a circle can be calculated using the formula:

A = π * r²

Where:
A is the area
π is a mathematical constant (approximately 3.14159)
r is the radius of the circle

Given:
Radius of the floodgate (r) = 0.5 m

A = 3.14159 * (0.5)²
A = 0.7854 m² (approximately)

Now, we can calculate the force:

Force = Pressure * Area
Force = 19132.4 * 0.7854
Force = 15047.1 N (approximately)

Therefore, the force exerted by the water on the floodgate is approximately 15047.1 N.

To calculate the force exerted by the water on the floodgate, you can use the concept of hydrostatic pressure.

Hydrostatic pressure is the pressure exerted by a fluid at a certain depth due to the weight of the fluid above it. The equation for hydrostatic pressure is given by:

P = ρ * g * h

Where:
P = Pressure (in Pascal)
ρ = Density of the fluid (in kg/m^3)
g = Acceleration due to gravity (on Earth, approximately 9.8 m/s^2)
h = Depth of the fluid (in meters)

In this case, the depth of the floodgate is 2 m, so the pressure exerted by the water at that depth is given by:

P = ρ * g * h
= 977 kg/m^3 * 9.8 m/s^2 * 2 m
= 19107.2 N/m^2 or Pascal

Now, to find the force exerted by the water on the floodgate, you need to calculate the area of the circular floodgate and multiply it by the pressure. The area of a circle is given by:

A = π * r^2

Where:
A = Area of the circle
π = Pi (approximately 3.14)
r = Radius of the floodgate

In this case, the radius of the floodgate is 0.5 m, so the area of the floodgate is:

A = π * r^2
= 3.14 * (0.5 m)^2
= 0.785 m^2

Finally, to calculate the force exerted by the water, you multiply the pressure by the area:

Force = P * A
= 19107.2 N/m^2 * 0.785 m^2
= 23050 N

Therefore, the force exerted by the water on the floodgate is 23050 N.