Final answer:
To determine the water pressure supplied by the faucet, we need to use Bernoulli's equation. The pressure at the faucet is equal to the pressure in the hose, but we cannot calculate the specific water pressure without knowing the pressure at which the water is supplied.
Step-by-step explanation:
To determine the water pressure supplied by the faucet, we need to use Bernoulli's equation. Bernoulli's equation states that the pressure of a fluid decreases as its velocity increases. Since the hose is nozzleless, the velocity of the water is constant throughout the hose. The pressure at the faucet is equal to the pressure in the hose.
The flow rate of the water is given as 50.0 L/s. In order to convert this to m³/s, we can use the conversion factor 1 L = 0.001 m³. Therefore, the flow rate is 0.05 m³/s.
The equation for Bernoulli's principle is:
P1 + 0.5ρv1² + ρgh1 = P2 + 0.5ρv2² + ρgh2
Where:
P1 and P2 are the pressures at points 1 and 2
ρ is the density of the fluid
v1 and v2 are the velocities at points 1 and 2
g is the acceleration due to gravity
h1 and h2 are the heights at points 1 and 2
Assuming the hose is horizontal and there is no change in height, the equation simplifies to:
P1 + 0.5ρv1² = P2 + 0.5ρv2²
Since the hose is nozzleless, the velocity at all points is the same. Therefore, we can simplify the equation further:
P1 = P2
So the water pressure supplied by the faucet is equal to the pressure in the hose. However, the question does not provide any information about the pressure at which the water is supplied. Without this information, we cannot calculate the specific water pressure supplied by the faucet.