Question

In: Physics

The water flow rate for a particular sprinkler is 16 gpm. The water must be projected...

The water flow rate for a particular sprinkler is 16 gpm. The water must be projected at least 25 feet in radius. The sprinkler is mounted 11 feet above the ground and is aimed at an angle of 29 degrees above the horiztonal. With what velocity must the water leave the sprinkler? What diameter (inches) should the opening be to achieve this velocity?

Solutions

Expert Solution

Let ,

R = maximum distance reached by the water

v = velocity of water leaving the sprinkler

h = height from which the water is projected

= angle of projection from the horizontal

Horizontal component of the velocity = vcos

Vertical component of the velocity = vsin

For horizontal motion

As there is no acceleration in the horizontal direction

Sx = uxt + (1/2)axt2

R = vcos×t + 0 ( as Sx = R and a​​​​​​x = 0 )

t = R/vcos ..............equation (1)

For vertical motion

Sy = uy​​​​t + (1/2)ayt2

h = -vsint + (1/2)gt​​​​​​2 ....  eq(2)

( as vsin is upwards so negative)

From equation (1) and (2)

h = -vsin(R/vcos) + (1/2)g×(R/vcos)2

h = -Rtan + gR2 / 2v2​​​​​​cos2

On putting the numerical values

11 = -25×tan29° + 32×(25)2/ 2×v2×cos229°

11 = -13.86 + 20000 / 2×v2×0.765

24.86 = 20000 / 2×v2×0.765

v2 = 525.82

v = 22.93 ft/s

From equation of continuity

Area of cross section × velocity = rate of flow of liquid

A × v = 16 gpm (gpm is gallon per minute)

A × 22.93 = (16×0.1336 /60 ) ft3/s

d2/4 = 0.0356 / 22.93 ( d = diameter of the pipe)

d​​​​​​2/4 = 0.00155

d2 = 0.001979

d = 0.0445 ft

d = 0.0445 × 12 inches

d = 0.534 inches


Related Solutions

The water flow rate for a particular sprinkler is 19 gpm. The water must be projected...
The water flow rate for a particular sprinkler is 19 gpm. The water must be projected at least 24 feet in radius. The sprinkler is mounted 11 feet above the ground and is aimed at an angle of 26 degrees above the horiztonal. With what velocity must the water leave the sprinkler? What diameter (inches) should the opening be to achieve this velocity? Water Velocity =_______ ft/s Diameter Opening = ______ inches
The water flow rate for a particular sprinkler is 18 gpm. The water must be projected...
The water flow rate for a particular sprinkler is 18 gpm. The water must be projected at least 22 feet in radius. The sprinkler is mounted 10 feet above the ground and is aimed at an angle of 29 degrees above the horiztonal. With what velocity must the water leave the sprinkler? What diameter (inches) should the opening be to achieve this velocity? Water Velocity = ft/s Diameter Opening =  inches
If the flow rate of soil waste is 205 GPM, what size drainpipe will be needed...
If the flow rate of soil waste is 205 GPM, what size drainpipe will be needed for: a. A slope of 1/2 inch per foot of fall? What is the flow rate of the drainpipe selected? b. A slope of 1 ∕8 inch per foot of fall? What is the flow rate of the drainpipe selected?
A 32 inch diameter pump handling 22000 GPM flow of water coming from an atmospheric tank...
A 32 inch diameter pump handling 22000 GPM flow of water coming from an atmospheric tank storage is running at 1170 rpm. The water temperature can be taken at 25 C. The suction line is 20 meter long at 6 inch diameter. The pump suction is 0.4 meter above ground level. The tank storage is elevated on a 1 meter high platform. Assume friction factor of 0.02. Specific Gravity of water at 25 C is 0.9967. NPSH required is 34...
Using the flow rate of 250 gpm, select a plastic pipe diameter (2”, 4”, 6”, 8”,...
Using the flow rate of 250 gpm, select a plastic pipe diameter (2”, 4”, 6”, 8”, 10”…) & determine the approximate pump head based on the following: Minor pipe losses include 6-90 degree bends (standard) and one plug valve straightway. Document your source for your K-values. Document which calculation method you used to calculate the total pump head. To save energy, choose the largest pipe diameter that provides the recommended 2.0 fps velocity of flow. Assume nominal pipe diameters as...
Design a system to move 100 gpm of water from a river with surface water elevation...
Design a system to move 100 gpm of water from a river with surface water elevation of 201.35 ft msl to a tank with surface water elevation = 246.55 ft msl. The tank is pressurized; the air pressure in the tank is 60 psig. The total length of pipe is 125 ft with 6 standard elbows all made of Sch 40 steel pipe. Your design should specify the nominal diameter of pipe (use only commercially available sizes) and the power...
We designed the water flow rate to supply water to the increased population in New Jersey...
We designed the water flow rate to supply water to the increased population in New Jersey in 2020 and the trapezoidal canal that conveys the increased amount of water resources like Figure 2. The concrete-lined canal (n=0.015) is to have a B (bottom width) /yn (B/yn) of 2.0, 2H:1V side slopes and a velocity of 5.0 feet/s. The normal water depth is 3.75 ft and the longitudinal slope is 0.000825.    2.1. When the depth of flow at the gaging...
A Rankine cycle uses water as its working fluid. The mass flow rate of water through...
A Rankine cycle uses water as its working fluid. The mass flow rate of water through the cycle is 150 kg/s. Superheated vapour exits the boiler at 8 MPa and 560 °C. The condenser pressure is 8 kPa. The water at the pump inlet is 35 °C. The isentropic efficiency of the pump is 75% and the isentropic efficiency of the turbine is 91%. The turbine and pump can be treated as adiabatic. The pressure drops of the working fluid...
Find the diameter of a pipe of length ‘X’ when the rate of flow of water...
Find the diameter of a pipe of length ‘X’ when the rate of flow of water through the pipe is ‘Q’ and the head lost due to friction is ‘4X’. Take the value of C = 1 in Chezy’s formula. Illustrate the resut of diameter of pipe and also conclude the discharge value for varying cross section of pipe, and the relationship between diameter of pipe and pressure of flow.
You explored the effect of flow rate of water in response to changes in tube diameter....
You explored the effect of flow rate of water in response to changes in tube diameter. Did your prediction of the what tube would give the fastest and slowest flow rate turn out to be correct after performing the experiment? If not, why were you surprised? (if you have not performed the experiment, make a prediction based on what you learned in the lecture how flow rate is affected by the radius of a tube and then watch the video...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT