physics
A rectangular open tank 6.0m × 8.0m is filled with water to a depth of 8.0m if the atmospheric pressure 1.013×10^pa.find the pressure at the bottom of the tank and force exerted at the bottom assume that g=10N/kg?
To find the pressure at the bottom of the tank and the force exerted at the bottom, we can use the concept of pressure in fluids. The pressure at any point in a fluid is given by the equation:
Pressure = Density × Gravity × Height
Where:
Density is the density of the fluid (in this case, water)
Gravity is the acceleration due to gravity (g = 10 N/kg)
Height is the vertical distance of the point from the reference point (in this case, the bottom of the tank)
Step 1: Calculate the pressure at the bottom of the tank.
Given the atmospheric pressure, which is 1.013 × 10^5 Pa, we need to add this to the pressure exerted by the column of water.
Pressure at the bottom = Atmospheric pressure + Pressure due to the water
Pressure at the bottom = 1.013 × 10^5 Pa + (Density × Gravity × Height)
Step 2: Calculate the force exerted at the bottom of the tank.
To calculate the force, we need to multiply the pressure at the bottom by the surface area of the tank.
Force = Pressure at the bottom × Surface Area
Surface Area = Length × Width
Let's plug in the given values:
Length = 6.0 m
Width = 8.0 m
Height = 8.0 m
Now, let's calculate the pressure at the bottom first using the density of water.
Density of water = 1000 kg/m^3 (approximately)
Pressure at the bottom = 1.013 × 10^5 Pa + (1000 kg/m^3 × 10 N/kg × 8.0 m)
Calculate the value of pressure at the bottom, and you will get your answer.