You hold a hose 45 degrees to the horizontal and at a height of 1 m from the floor. The water reaches a maximum distance of 10 m from where you are standing. Now you place your thumb over the end of the hose to occlude the opening by 80%, which in turn reduces the flow rate by 50%. Even though less fluid emerges the water travels further. How far does the water travel with your thumb over the end of the hose? Find the amount by which the hose must be occluded in order for the water to travel twice as far.

Question

You hold a hose 45 degrees to the horizontal and at a height of 1 m from the floor. The water reaches a maximum distance of 10 m from where you are standing. Now you place your thumb over the end of the hose to occlude the opening by 80%, which in turn reduces the flow rate by 50%. Even though less fluid emerges the water travels further. How far does the water travel with your thumb over the end of the hose? Find the amount by which the hose must be occluded in order for the water to travel twice as far.

Answer 1

convert this into a projectile problem.

First solve for velocity of projectile needed to reach ground at 10 meters when fired at 45 deg from height of 1 m
Call that V1

Now find V2, the new velocity
Q2 = .5 Q1 = .5 * V1 * A1
and Q2 = V2 A2 so
V2 = .5 V1 (A1/A2) = .5*(1/.2) * V1 = 2.5 V1

Answer 2

To find how far the water travels with your thumb over the end of the hose, we will need to consider the principles of fluid flow and the impact of occluding the hose opening.

First, let's break down the problem step by step:

1. Initial conditions: The hose is held at a 45-degree angle to the horizontal and the water reaches a maximum distance of 10 m from where you are standing.

2. Occluding the opening: By placing your thumb over the end of the hose, you occlude the opening by 80%. This means that only 20% of the original opening area is available for the water to flow through.

3. Reduced flow rate: With the occlusion, the flow rate is reduced by 50%. This means that only half the volume of water is coming out per unit of time compared to the initial condition.

Now let's determine the effect of these changes on the water's travel distance:

1. Occluded opening: When the hose opening is occluded by 80%, the water stream will experience an increase in velocity due to the reduced flow area. The increased velocity allows the water to travel further, even though less fluid is emerging.

2. Reduced flow rate: By reducing the flow rate by 50%, the water stream will have more time to accelerate before it reaches the maximum distance. As a result, the water will be able to travel even further compared to the initial condition.

To calculate the new distance, we need to consider the changes in velocity and time:

1. Velocities: The velocity of the water stream when the hose is not occluded (initial condition) and when the hose is occluded (with your thumb over the end) will be different. However, since both velocities are unknown, we cannot directly compare them. We will need additional information to determine the specific velocity changes.

2. Time: When the flow rate is reduced by 50%, it will take twice as long for the same volume of water to emerge compared to the initial condition. This additional time allows the water to travel a greater horizontal distance.

Therefore, to determine the exact distance the water travels with your thumb over the end of the hose, we would need specific information on the velocity changes resulting from the occlusion.