A water hose 2.85 cm in diameter is used by a gardener to fill a 28.0-liter buck

Question

A water hose 2.85 cm in diameter is used by a gardener to fill a 28.0-liter bucket. (One liter = 1,000 cm3.) The gardener notices that it takes 1.00 min to fill the bucket. A nozzle with an opening of cross-sectional area 0.500 cm2 is then attached to the hose. The nozzle is held so that water is projected horizontally from a point 1.00 m above the ground. Over what horizontal distance can the water be projected?
4.22 m **Correct**

Use the values from above to help you work this exercise. The nozzle is replaced with a Y-shaped fitting that splits the flow in half. Garden hoses are connected to each end of the Y, with each hose having a 0.420 cm2 nozzle.

(a) How fast does the water come out of one of the nozzles?
?? m/s
Some of the information you need is in the example. m/s

(b) How far would one of the nozzles squirt water if both were operated simultaneously and held horizontally 1.00 m off the ground? (Hint: Find the volume flow rate through each 0.420-cm2 nozzle, then follow the same steps as before.)
? m

Show Work Please

Explanation / Answer

the volume flow rate is calculated as follows:

Q = dV/dt = [28 L/1 min]= 28x10-3/60 = 4.67x10-4 m3/s

the volume flow rate at one nozzle is,

Q' = (1/2)dV/dt

from contnuity equation, we eget

Av0x =  (1/2)dV/dt

hence, the required speed is,

v0x = (1/2A)dV/dt = (1/2*0.5X10-4)[ 4.67x10-4] = 4.67 m/s

----------------------------------------------------------------------------------------------------------

the time t is,

t = sqrt[2y/g] = sqrt[2*1/9.8] = 0.45175 s

the horizontal distance is,

d = v0xt = 4.67*0.45175 = 2.11 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.