Please help! Any advice is appreciated

A water faucet in a house is h=8 m below the water surface in the local water tower. The
radius of the orifice in the fully opened faucet is r=0.01 m. We assume non-viscous flow
in this problem.
a) How long does it take to fill a 20 liter bucket with water using this faucet.

(1/2) m v^2 = m g h

or use Bernoulli
(1/2) rho v^2 + rho g h + P = constant
here P = 1 atm on top of the tank and at the outflow so the two ways are the same
v = sqrt (2 g h ), just like the water fell
amount that comes out per second = Q = Area*v = pi r^2 v = pi*10^-4 v
so
Q = pi*10^-4* sqrt(2*9.81*8)
20 liters = .02 m^3 = Q t
so
t= .02/[pi*10^-4*sqrt(2*9.81*8)]

To find out how long it takes to fill a 20 liter bucket with water using this faucet, we can use the equation for the volume of water flowing through the faucet per unit time.

The volume flow rate of water can be calculated using the equation:

Q = A * v

Where:
Q is the volume flow rate (m^3/s)
A is the cross-sectional area of the orifice (m^2)
v is the velocity of water flowing through the orifice (m/s)

We need to convert the volume of water in liters to cubic meters. Since 1 liter is equal to 0.001 cubic meters, the volume of water in the bucket is 20 * 0.001 = 0.02 cubic meters.

To find the velocity of the water, we can use Bernoulli's equation for the conservation of energy, which ignores any losses due to friction:

P + 1/2 * ρ * v^2 + ρ * g * h = constant

Where:
P is the pressure of the water at the orifice (Pa)
ρ is the density of water (kg/m^3)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height difference between the orifice and water surface (m)

Assuming the pressure at the orifice is atmospheric pressure, we can simplify the equation to:

1/2 * ρ * v^2 = ρ * g * h

Canceling out ρ (density of water) from both sides of the equation, we get:

1/2 * v^2 = g * h

Solving for v, we have:

v = √(2 * g * h)

Now, using the equation for volume flow rate:

Q = A * v

Substituting the values of A (π * r^2) and v (√(2 * g * h)), we get:

Q = π * r^2 * √(2 * g * h)

Finally, we can calculate the time it takes to fill the bucket using the volume flow rate and the volume of water in the bucket:

t = Volume / Q

Substituting the values, we get:

t = 0.02 / (π * r^2 * √(2 * g * h))

Plugging in the given values for r, h, and g, we can calculate the time it takes to fill the 20-liter bucket with water using this faucet.