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Liquid water flows isothermally at 20°C through a one-inlet, one-exit duct operating at steady state. The duct’s inlet and exit diameters are 0.02 m and 0.1 m, respectively. At the inlet, the velocity is 10 m/s and pressure is 1 bar. At the exit, determine the mass flow rate, in kg/s, and velocity, in m/s.
Liquid water flows isothermally at 20°C through a one-inlet, one-exit duct operating at steady state. The duct’s inlet and exit diameters are 0.02 m and 0.1 m, respectively. At the inlet, the velocity is 10 m/s and pressure is 1 bar. At the exit, determine the mass flow rate, in kg/s, and velocity, in m/s.
Thecontinuity equationallows finding the results for the speed and flow of the outlet pipe are:Q = 3.14 kg / sv₂ = 0.4 m / sFluid mechanicsstudies the movement andfluid dynamics, it is described by two fundamental relationships:TheBernoulliequation that an expression of theenergy conservationWhere P is the pressure, v the velocity, y the height, the subscripts are two selected points of interest in the pipe.Thecontinuity equationwhich is an expression that our principle ofmass conservationfor fluidsWhere A₁ and A₂ is the area of the inlet and outlet pipes and v₁ and v₂ are the velocities of the fluid at the inlet and outletThey indicate the inlet and outletdiametersof thepipeare d₁ = 0.02 m and d₂ = 0.1 m, the inletvelocityv₁ = 10 m / s, with the continuity equation let's find theoutlet velocitythe cross section of the tavern isA =Where r is the radius and d is the diameterLet's substitutesv₂ = 0.4 m / sTheflow(Q) is defined as theamountof liquid thatpassesthrough thesectionof thepipeper unit oftime,we can see that this is the same conservation of mass, thereforeQ = A vQ =π d2 ^ 2 v2Q =Q = 3.14 10⁻³ m ^ 3 / sAs the transported liquid iswater1 liter water = 1 kgConsequently1 m³ = 1000 liter = 1000 kg of waterLet's reduce the flowQ = 3.14 10⁻³ m³/s ()Q = 3.14 kg / sIn conclusion using thecontinuity equationwe can find the results for the speed and flow of the outlet pipe are:v₂ = 0.4 m / sQ = 3.14 kg / sLearn more here:brainly.com/question/14747327...