How Many Holes Are Needed in a Bottle to Effectively Water a Garden?

[eraldcoil]

A garden is watered with a watering homemade consist of a plastic bottle, with numerous holes $$r$$ of diameter, lying on the garden and conected to a hose. Asumme that a bomb water is responsible for generating a flow of water constant $$Q$$. How many holes must have the bottle to get water to wet the meadow to $$D$$ distance from the bottle? Whats is the pressure inside the hose f it has across section $$A.$$?

The only thing I miss is:

$$v$$:speed with which water comes out of each dimple.ec continuity:

$$Q=nAv$$, $$n$$: number of holes.

$$v=Q/(nA)$$

and do not know what else to do...

thanks in advance.

 

[jbsteele]

Assuming that the water is released from the holes in a uniform manner, you can use the continuity equation to calculate the number of holes required. The continuity equation states that the flow rate (Q) is equal to the number of holes (n) multiplied by the area of each hole (A) multiplied by the velocity of the water coming out of each hole (v). Therefore:Q = nAvSince we know the flow rate (Q) and the area of each hole (A), we can solve for the number of holes (n)n = Q/(Av)Once you have calculated the number of holes, you can determine the pressure inside the hose by using Bernoulli's equation. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy along a streamline is constant. Therefore, the pressure at the end of the hose (where the water is being released onto the meadow) will be equal to the pressure of the water inside the bottle plus the pressure losses due to friction as the water travels through the hose. The pressure losses due to friction can be calculated using the Darcy-Weisbach equation.Hope this helps!