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A conical funnel of half-angle θ = 30° drains through a small hole of diameter d = 6.25 mm. at the vertex. The speed of the liquid leaving the funnel is
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- A brand of toothpaste is made using a mixture of white and red paste. During the manufacturing process, both pastes are pumped through a pipe, with the red paste lying in the centre of the pipe, as shown in Figure Q2. The pipe has an internal radius, R₂, and the segment of red paste has a radius R₁. The flow is found to follow the Poiseuille equation, i.e. u(r) = 1 dp - (R² - r²) dp Where u is the viscosity of the paste and μ is the pressure gradient. The total flow of toothpaste through the pipe is Qtot, and the flowrate of the red paste is Qred. dx 4μ dx The toothpaste has a density of p = 1200 kg/m³, and a viscosity of 0.03 Pa.s. The pipe has a radius R₂ = 5 cm and a length L = 2 m. R₁ a) Find an expression for the flowrate of the red toothpaste. You answer should be in terms of µ, R₁, R₂, P) b) The flow in the pipe becomes turbulent when the Reynolds number reaches 2000 (where Re is calculated using the mean velocity across the pipe). What is the maximum pressure drop along the…arrow_forwardA piston 46mm in diameter slides concentrically in a fixed cylinder 50mm in diameter. The cylinder is filled with water and when the piston moves into the annular gap, water flows through the annular gap surrounding the piston. If the velocity of piston is 75mm/s raletive to the cylinder, determine the velocity of flow through the gap.arrow_forwardThe head of water at the Inlet of a pipe of length 1500 m and diameter 400 mm is 50 m. A nozzle of diameter 80 mm at the outlet, is fitted to the pipe. Find the velocity of water at the outlet of the nozzle if f=0.01 for the pipe.arrow_forward
- Water is discharged from a reservoir into the atmosphere through a 80 m long pipe. There is a sharp entrance to the pipe and the diameter is 250 mm for the first 50 m. The outlet is 35 m below the surface level in the reservoir. The pipe then enlarges suddenly to 450 mm in diameter for the reminder of its length. Take f 0.004 for both pipes. Calculate the discharge.arrow_forwardFind an expression for the velocity of water leaving the sprinkler. Find an expression for the gauge pressure at point A, a distance L1, upstream of the narrow pipes. Express the answer in terms of the flowrate, Q. The inner diameter of the first segment of the pipe is d1=10mm, the inner diameter of the second set of pipes is d2=1mm, with N=25. The flowrate through the sprinkler is Q=0.2 L/s. Flow in pipes typically becomes turbulent when the Reynolds number exceeds 2000. Comment on the accuracy of the assumption that the flow could be treated as laminar everywhere. May be assumed water has a density of 1000kg/m^3 and a viscosity of 1mPa s.arrow_forwardA horizontal nozzle discharges water into the atmosphere as shown in the figure. the relative pressure at point 1 equal to p1 = 18 kPa. a. A Pitot tube connected to a mercury manometer is inserted into the flow. in the area section A1 indicating a height difference h = 0.01 m. For this reading indicated in the Pitot tube, determine the velocity in the A1 area section of the nozzle. b. For the dimensioning of the anchor block it is necessary to determine the force that the nozzle applies over the fluid. Calculate the component of this force in the x direction. Data: D1 = 0.070 m; D2 = 0.060 m; 0 = 30°; dHg = 13.6 Patm A2 pi Fx A1 Block of anchoragearrow_forward
- A pipe 5 m long is inclined at 15° with horizontal.The smaller section of the pipe is in 80 mm diameter & at lower level whereas other section is 240 mm diameter. Determine the difference of pressure between two sections. Pipe is uniformly tapering & the velocity of water at smaller section is 1 m/s. Also show the direction of flow of water. 5 m 0 = 15° datum line 2.arrow_forwardA venturi meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe (the figure); the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed Vand then through a narrow "throat" of cross-sectional area a with speed v. A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid's speed is accompanied by a change Ap in the fluid's pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here Ap means pressure in the throat minus pressure in the pipe.) Suppose that the fluid is fresh water, that the cross- sectional areas are 93 cm2 in the pipe and 31 cm² in the throat, and that the pressure is 53 kPa in the pipe and 44 kPa in the throat. What is the rate of water flow in cubic meters per second? Meter Meter entrance Venturi meter exit A…arrow_forwardWater flows from a nozzle with a speed of V = 10m/s Stream diameter = 0.1 m Nozzle -- Moving control volume and is collected in a container that moves toward the V = 10 m/s nozzle with a speed of Vcy = 2 m/s as shown in the figure. If the water between the nozzle and the tank is in the constant diameter stream, what is the accumu- V = 2 m/s 3 m lation rate of water in the tank?arrow_forward
- When a pitot tube as shown below is placed in a river with its lower open end facing upstream, water rises in the vertical portion to a height of 50mm above the water surface. Find the flow velocity U. [density of water ρ = 1000kg/m3]arrow_forwardThe figure represents a stream of water in a pipe. If the distribution of velocities in a section is given by v (see picture) where beta is a constant, r is the radial distance to the axis, and v is the velocity a at distance r from the axis, determine the flow rate Q.Sarrow_forwardThe water of a 14’ × 48’ metal frame pool can drain from the pool through an opening at the side of the pool. The opening is about h = 1.05 m below the water level. The capacity of the pool is V = 3740 gallons, the pool can be drained in t = 10.2 mins. P0 is the pressure of the atmosphere. ρ is the density of the water. a. Write the Bernoulli’s equation of the water at the top of the pool in terms of P0, ρ, h. Assuming the opening is the origin. b. Write the Bernoulli’s equation of the water at the opening of the pool in terms of P0, ρ, h and v, where v is the speed at which the water leaves the opening. Assuming the opening is the origin. c. Express v2 in terms of g and h. d. Calculate the numerical value of v in meters per second. e. Express the flow rate of the water in terms of V and t. f. Express the cross-sectional area of the opening, A, in terms of V, v and t. g. Calculate the numerical value of A in cm2arrow_forward
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