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
Sure, I'd be happy to help you with this question!
To calculate the force exerted by the water on the floodgate, we can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above it.
In this case, the force exerted by the water on the floodgate is equal to the pressure exerted by the water multiplied by the area of the floodgate.
First, let's calculate the hydrostatic pressure at the depth of the floodgate. The hydrostatic pressure is given by the formula:
P = ρgh
Where:
P is the pressure,
ρ is the density of the fluid,
g is the acceleration due to gravity,
and h is the depth below the surface of the fluid.
In this case, the density of water is given as 977 kg/m^3, and the depth of the floodgate is 2 m. The acceleration due to gravity is approximately 9.8 m/s^2.
Let's plug in these values and calculate the hydrostatic pressure:
P = (977 kg/m^3) * (9.8 m/s^2) * (2 m) = 19116.4 N/m^2
Next, we need to calculate the area of the floodgate. The area of a circle is given by the formula:
A = πr^2
Where:
A is the area,
π is a mathematical constant (approximately 3.14),
and r is the radius of the floodgate.
In this case, the radius of the floodgate is given as 0.5 m. Let's calculate the area:
A = π * (0.5 m)^2 = 0.7854 m^2
Finally, we can calculate the force exerted by the water on the floodgate by multiplying the pressure by the area:
Force = Pressure * Area
Force = (19116.4 N/m^2) * (0.7854 m^2) = 15053.6 N
So, the force exerted by the water on the floodgate is approximately 15053.6 N.
I hope this helps you understand the concept! Let me know if you have any further questions or if there's anything else I can assist you with.