Answer: approximately 68,404 liters.
Explanation:
To solve the problem, we first need to find the cross-sectional area of the pipe, which we can calculate using the formula for the area of a circle:
A = πr^2
where r is the radius of the pipe, which is half the diameter. So, in this case, the radius is 2.4 cm / 2 = 1.2 cm.
A = π(1.2 cm)^2
A ≈ 4.5239 cm^2
Next, we can use the formula for volume flow rate to find the volume of water that is discharged per second:
Q = Av
where Q is the volume flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the water. In this case, we have:
Q = (4.5239 cm^2)(2.8 m/s)
Q ≈ 0.01266 m^3/s
To find the volume of water discharged in one and a half hours (which is 5400 seconds), we can multiply the volume flow rate by the time:
V = Qt
V = (0.01266 m^3/s)(5400 s)
V ≈ 68.404 m^3
Finally, to convert the volume from cubic meters to liters, we can multiply by 1000:
V = 68.404 m^3 × 1000 L/m^3
V ≈ 68,404 L
Therefore, the volume of water discharged in one and a half hours is approximately 68,404 liters.