When the end of a particular garden hose is held at a height of 1m, water flows out of it at 8 cm/s. What is the difference in fluid pressure between the end of the hose and a portion resting on the ground? Suppose I cover half of the area at the end with my thumb. What maximum vertical height would the spray reach is the hose was pointed straight upward?

Question

When the end of a particular garden hose is held at a height of 1m, water flows out of it at 8 cm/s. What is the difference in fluid pressure between the end of the hose and a portion resting on the ground? Suppose I cover half of the area at the end with my thumb. What maximum vertical height would the spray reach is the hose was pointed straight upward?

Answer 1

To find the difference in fluid pressure between the end of the hose and a portion resting on the ground, we can use the equation for fluid pressure:

Pressure = Density × Gravity × Height

Since the portion of the hose resting on the ground is at the same height as the reference level, its height value would be considered zero. Therefore, the pressure at that point is zero. The height of the end of the hose is given as 1 meter.

To find the pressure at the end of the hose, we need to know the density of the fluid flowing through it. Let's assume it's water, which has a density of approximately 1000 kg/m³. The acceleration due to gravity is approximately 9.8 m/s².

Substituting the values into the formula, we get:

Pressure = (1000 kg/m³) × (9.8 m/s²) × (1 m)
= 9800 Pascal (Pa)

Therefore, the difference in fluid pressure between the end of the hose and the portion resting on the ground is 9800 Pa.

Now, let's consider the second part of your question. If you cover half of the area at the end of the hose with your thumb, it means only half of the water flow will exit the nozzle. The remaining portion is blocked by your thumb.

Since the water flow velocity is given as 8 cm/s, the maximum vertical height the spray would reach can be calculated by using the projectile motion equation. You can treat the water as a projectile that follows a parabolic trajectory.

Assuming no air resistance, the equation for maximum vertical height (h) is:

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

where v is the initial vertical velocity and g is the acceleration due to gravity.

Let's find v using the given flow velocity:

v = 0.5 × 8 cm/s
= 4 cm/s
= 0.04 m/s

Substituting the values into the equation, we get:

h = (0.04 m/s)^2 / (2 × 9.8 m/s^2)
≈ 8.16 × 10^(-4) m
≈ 0.82 cm

Therefore, if the hose is pointed straight upward, the maximum vertical height the spray would reach is approximately 0.82 cm.