Question

You hold a hose at 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?
a) How far does the water travel with your thumb over the end of the hose (assuming the height and
angle remain the same)?
b) Assume the flow rate (as a percentage of original flow rate) can given by
Q%=100[1-(A/100)^5]
where A% is the percentage by which the opening of the hose is occluded. Notice that if A% is 0% then Q%
is 100%, whereas if A% is 100% then Q% is 0%. Find the amount by which the hose must be
occluded in order for the water to travel twice as far (assuming the height and angle remain the same).