a homeowner wishes to drain her swimming pool by siphoning the water,whose depth is h,into a nearby gully a distance H below it,where H is much larger than h.She uses a pipe of cross-sectional areea a,and the pool has surface area A.How long does it take to empty the pool if h=2m,H=20m,A=50meter squad,a=5centi meter squad?

Bernoulli's equation applies. Solve for flow rate.

To calculate the time it takes to drain the swimming pool by siphoning the water, we first need to understand the principles of siphoning and the relevant formulas.

1. Determine the difference in height: In this case, the difference in height is H - h, which is 20m - 2m = 18m.

2. Calculate the flow rate of water through the pipe: The flow rate (Q) can be determined using the Torricelli's Law, which states that the flow rate is proportional to the square root of the difference in height.

Q = a * √(2 * g * (H - h))

where:
Q = Flow rate of water (m³/s)
a = Cross-sectional area of the pipe (m²)
g = Acceleration due to gravity (9.8 m/s²)

In this case, the cross-sectional area of the pipe is given as a = 5 cm² = 5 × 10^(-4) m² and the acceleration due to gravity is g = 9.8 m/s².

Plugging in the values:
Q = (5 × 10^(-4)) * √(2 * 9.8 * 18) ≈ 0.0502 m³/s

3. Calculate the volume of the pool: The volume (V) of the pool can be calculated by multiplying the surface area (A) of the pool by the depth (h).

V = A * h

In this case, the surface area is given as A = 50 m² and the depth as h = 2 m.

Plugging in the values:
V = 50 * 2 = 100 m³

4. Calculate the time to drain the pool: The time (t) to drain the pool can be calculated by dividing the volume of the pool by the flow rate.

t = V / Q

Plugging in the values:
t = 100 / 0.0502 ≈ 1992 seconds

Therefore, it would take approximately 1992 seconds, or about 33.2 minutes, to drain the swimming pool using the given parameters.