Four lawn sprinkler heads are fed by a 1.9 cm diameter pipe. The water comes out

Question

Four lawn sprinkler heads are fed by a 1.9 cm diameter pipe. The water comes out of the heads at an angle of 39° to the horizontal and covers a radius of 7.6 m.

(a) What is the velocity of the water coming out of each sprinkler head? (Assume zero air resistance.)______m/s

(b) If the output diameter of each head is 3.0 mm, how many liters of water do the four heads deliver per second?_______L/s

(c) How fast is the water flowing inside the 1.9 cm diameter pipe?________m/s

The answers aren't (a) 9.77m/s (b) 0.000276 L/s (c) 0.43 m/s

Here's a practice problem with the correct answers for reference:

Four lawn sprinkler heads are fed by a 1.9 cm diameter pipe. The water comes out of the heads at an angle of 37° to the horizontal and covers a radius of 8.4 m

(a) 9.25 m/s

(b) 0.262 L/s

(c) 0.923 m/s

Thanks!

Explanation / Answer

Given

Range = 7.6 m

theta = 39 degrees

a) let v2 is the speed of water through sprinler.

we know,

horizontal range, R = v2^2*sin(2*theta)/g

v2^2 = R*g/sin(2*theta)

v2= sqrt(R*g/sin(2*theta))

= sqrt(7.6*9.8/sin(2*39))

= 8.73 m/s

b) Volume flow rate = 4*A2*v2

= 4*(pi*d2^2/4)*v2

= 4*(pi*(3*10^-3)^2/4)*8.73

= 0.247*10^-3 m^3/s

= 0.247 L/s

c) Use Continuty equaltion

A1*v1 = 4*A2*v2

v1 = 4*v2*(A2/A1)

= 4*v2*(pi*d2^2/4)/(pi*d1^2/4)

= 4*v2*(d2/d1)^2

= 4*8.73*(0.3/1.9)^2

= 0.87 m/s

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