108k views
4 votes
Water exits a garden hose at a speed of 1.2 m/s. If the end of the garden hose is 1.5 cm in diameter and you want to make the water go 15 m high, what fraction of the area of the hole do you have to block off with your thumb?A : 93%B : 14%C : 7.0%D : 73%E : 27%

User Dragoweb
by
7.1k points

1 Answer

5 votes

Answer:

A 93%

Step-by-step explanation:


P_1=P_2 = Pressure will be equal at inlet and outlet


\rho = Density of water = 1000 kg/m³

g = Acceleration due to gravity = 9.81 m/s²


v_1 = Velocity at inlet = 1.2 m/s


v_2 = Velocity at outlet


r_1 = Radius of inlet =
(1.5)/(2)=0.75\ cm


r_2 = Radius of outlet

From Bernoulli's relation


P_1+(1)/(2)\rho v_1^2+\rho gh_1=P_2+(1)/(2)\rho v_2^2+\rho gh_2\\\Rightarrow (1)/(2)\rho v_1^2+\rho gh_1=(1)/(2)\rho v_2^2+\rho gh_2\\\Rightarrow v_2=\sqrt{2((1)/(2)v_1^2+gh_1-gh_2)}\\\Rightarrow v_2=\sqrt{2((1)/(2)1.2^2+9.81* 15)}\\\Rightarrow v_2=17.19709\ m/s

From continuity equation


A_1v_1=A_2v_2\\\Rightarrow \pi r_1^2v_1=\pi r_2^2v_2\\\Rightarrow r_2=\sqrt{(r_1^2v_1)/(v_2)}\\\Rightarrow r_2=\sqrt{(0.0075^2* 1.2)/(17.19709)}\\\Rightarrow r_2=0.00198\ m

The fraction would be


(A_1-A_2)/(A_1)* 100=(r_1^2-r_2^2)/(r_1^2)* 100\\ =(0.0075^2-0.00198^2)/(0.0075^2)* 100\\ =93.0304\ \%

The fraction is 93.0304%

User Codure
by
6.7k points