Repeat Prob. 6-56 for a water flow rate of 60 L/s.
(a)
The rotational speed of the sprinkler.
Answer to Problem 57P
The rotational speed of the sprinkler is
Explanation of Solution
Given information:
The volume flow rate of the water is
Write the expression for the velocity at the smaller section of the sprinkler.
Here, the cross sectional area at the smaller section of the sprinkler is
Write the expression for the velocity at the larger section of the sprinkler.
Here, the cross sectional area at the larger section of the sprinkler is
Write the expression for the velocity of the jet with respect to smaller jet.
Here, the distance of the smaller jet from the axis of rotation is
Write the expression for the velocity of the jet with respect to larger jet.
Here, the distance of the larger jet from the axis of rotation is
Write the expression for the absolute velocity of the water with respect to larger section of sprinkler.
Write the expression for the absolute velocity of the water with respect to smaller section of sprinkler.
Write the expression for the mass flow rate of the water at larger section of sprinkler.
Here, the density of the water is
Write the expression for the mass flow rate of the water at smaller section of sprinkler.
Here, the cross sectional area at the smaller section is
Write the expression for the mass flow rate of the water.
Here, the volume flow rate of the water is
Write the expression for the total mass flow rate.
Write the expression for the discharge for the smaller section.
Write the expression for the discharge for the larger section.
Write the expression for the angular speed using the angular momentum equation.
Write the expression for the rotation speed of the sprinkler.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The rotational speed of the sprinkler is
(b)
The total torque required to prevent the sprinkler.
Answer to Problem 57P
The total torque required to prevent the sprinkler is
Explanation of Solution
Write the expression for the torque on the sprinkler due to the larger jet.
Write the expression for the torque on the sprinkler due to the smaller jet.
Write the expression for the total torque.
Write the expression for the mass flow rate for the smaller section.
Write the expression for the mass flow rate for the larger section.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The total torque required to prevent the sprinkler is
Want to see more full solutions like this?
Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
- Consider laminar flow of water in a 0.9-cm-diameter pipe at a rate of 1.15 L/min. The velocity (m/s) of water halfway between the surface and the center of the pipe is ?arrow_forwardGasoline (? = 680 kg/m3 and ? = 4.29 × 10−7 m2/s) is transported at a rate of 240 L/s for a distance of 2 km. The surface roughness of the piping is 0.03 mm. If the head loss due to pipe friction is not to exceed 10 m, determine the minimum diameter of the pipe.arrow_forwardConsider a flow of SAE 30W oil at 20°C through a 2.4-cm-diameter smooth pipe at 1 million N/h. Determine the Reynolds number for this flow. For SAE 30W oil at 20°C, take ρ = 891 kg/m3, μ = 0.29 kg/m-s, and π = 22/7. The Reynolds number isarrow_forward
- Water is transported by gravity through a 10-cmdiameter 550-m-long plastic pipe with an elevation gradient of 0.01 (i.e., an elevation drop of 1 m per 100 m of pipe length). Taking ? = 1000 kg/m3 and ? = 1 × 10−6 m2/s for water, determine the flow rate of water through the pipe. If the pipe were horizontal, what would the power requirements be to maintain the same flow rate?arrow_forwardA small centrifugal pump is used to pump 30-Celsius water at the rate of 6 L/s with ahead of 44.54 m. If the diameter of the pump is 20 cm and operate at 1200 rpm,determine;(i) head coefficient,(ii) capacity coefficient, and(iii) power coefficient. also the same small centrifugal pump is used to pump water at same rate but with a temperature of 15-Celsius. determine in which condition (15-Cor 30-C) is the pump perform better in term of;(i) power out, and(ii) pump efficiency.Justify your answer.arrow_forwardConsider an air solar collector that is 1 m wide and 4 m long and has a constant spacing of 3 cm between the glass cover and the collector plate. Air flows at an average temperature of 45°C at a rate of 0.12 m3/s through the 1-m-wide edge of the collector along the 4-m-long passageway. Disregarding the entrance and roughness effects and the 90° bend, determine the pressure drop in the collector.arrow_forward
- Engine oil at 20 C flows in a 14-cm-diameter pipe at a rate of 900 L/min. The friction factor for this flow isarrow_forwardA 1.0 m radius cylindrical industrial tank filled with viscous oil to a level at a height h from its base, must be drained through a tube with a radius of 0.2 m and length L, connected to its base. The speed profile of oil in the drain tube can be described by the equation below. Where v is the oil speed, vmax is a = maximum oil speed, r is the radius, and R is the tube radius. Considering this problem situation, do what is asked in the following items, justifying your answers. a) What is the volume, in liters, of oil removed from the tank after 10 seconds, if the maximum discharge speed does the oil reach 0.35 m/s? Data: π ≈ 22/7; 1 m3 = 1000 L. b) What flow regime does the system operate? Demonstrate. Data: specific mass of oil = 800 kg/m3, specific mass of water = 1000 kg/m3, oil viscosity = 0.056 Pa.s e viscosity of water = 0.001 Pa.s.arrow_forwardWhich has a greater minor loss coefficient during pipe flow: gradual expansion or gradual contraction? Why?arrow_forward
- The rate of flow of water through a cylindrical tube that has an inner radius of 1.2 cm is 2791 cm3 in 88s at 293 K. Determine if the flow laminar or turbulent.arrow_forwardWhat are the primary considerations when selecting a flowmeter to measure the flow rate of a fluid?arrow_forwardA highly viscous liquid discharges from a large container through a small-diameter tube in laminar flow. Disregarding entrance effects and velocity heads, obtain a relation for the variation of fluid depth in the tank with time.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning