Methane in the gaseous state flows at a rate of 0.072 m^3/s in a pipe at a temperature of 27°C and gauge pressure of 148.675kPa (point 1). The pipe is divided into two branches (point 2 and 3), as seen in the figure. If the exit velocity in pipe 3 is 12 m/s with a density of 1.9 kg/m^3, what is the flow rate and velocity in pipe 2? Consider that in section 2 the fluid is leaving with a temperature of 402°C and an absolute pressure of 175 kPa. We have an atmospheric pressure of 101.325 kPa and R_methane = 0.5182 kJ/kg ⚫K. (1) Inflow D1 D3=50mm D2=100mm (3) (2)

Q1: A water tower is an elevated structure supporting a water tank constructed at a height sufficient to pressurize a distribution system for potable water. A completely filled and pressurized water tank was found with a small leakage (a hole 5cm in diameter) located on the sidewall of the tank, around 5 meters below the top of the tank. Please calculate the velocity of leakage water that discharges to the normal atmosphere. The dimension of the tank is 20-meter in height and 10-meter in diameter. The gauge pressure of the water tank top is 0.1M Pa. The Bernoulli equation is: P₁/pg + V₁²/2g +h₁ = P₂/pg + V₂²/2g +h₂ Gauge Pressure: 0.1 M Pa 5 meters Leakage velocity?

Your team is designing a chemical processing plant. You are the liquid handling and transportation specialist, and you need to transport a solvent (μ = 3.1 cP, ρ = 122k kg/m3) from a storage tank to a reaction vessel. Due to other equipment constraints, the fluid velocity must be 0.8 m/sec, and you must use stainless steel piping (ε = 0.00015 mm) with a total length (L) of 12 m. Determine the pipe inner diameter (ID) you will need to achieve a pressure drop of 0.3 kPa. Use the Moody chart.

Problem Consider a cylindrical pipe of length L and diameter D = 2R. The angle that the axis of the pipe forms with the vertical direction is a. Assume that when the fluid enters the pipe its velocity is uniform (i.e., it has the same value over the entire cross-section of the pipe) and equal to U in the axial direction. In the radial and angular directions, the velocity is zero. So, it is: 2 =0: v(r, 0, 2) = Ue, (1.1) Here v is the fluid velocity and e, is a vector of unit magnitude parallel to the coordinate axis z; furthermore, we have assumed that the pipe inlet is located at z = 0. Near the entrance of the pipe, the velocity profile varies in the axial direction. But after a certain entrance length, the profile becomes fully developed, no longer changing with z. The evolution of the velocity profile is sketched in Fig. 1, where, for clarity, the pipe inclination is not shown. The entrance length is denoted by L.. For z > L., the fluid velocity is no longer a function of the axial…

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A room has a volume of 349 m3. An air-conditioning system is to replace the air in this room every 81.5 minutes, using ducts that have a square cross section. Assuming that air can be treated as an incompressible fluid, find the length of a side of the square if the air speed within the ducts is (a) 2.00 m/s and (b) 7.00 m/s.   a:  b:

Please help me with this fluid mechanics question! Thank you!! :) A 1967 Harley-Davidson Shovelhead motorcycle uses a ventruri-carburetor to mix air and fuel for combustion. The venturi reduces the pressure to draw fuel from a reservoir chamber and to mix with the airstream as shown in the figure. The energy loss of the metering line is given by hL= (K*V^2)/2where K = 6.0 and V is the fuel velocity in the metering line. Assume that the air is an ideal fluid (68°F). Calculate the mass flux of air and the mass flux of fuel. Hint: Assume the air intake velocity is negligible.

Water is being pumped the through one inch diameter piping arrangement to a higher elevation (5 meters up). Assume incompressible fluid conditions and some heat losses to the surroundings. At the inlet water pressure is 1 bar, temperature 15C, and volumetric flow rate is 0.02 m3/s. At the exit pressure is 2.2 bar, temperature is 10C and velocity of the stream is 40 m/s. Determine: a.Density of the inlet stream using NIST tables.  b.Mass flow rate [kg/s] c.Determine h2 from known p2 and T2 using NIST tables d.Find heat rate removed from Q=m(h1-h2) Use Energy Balance Equation with enthalpy difference and in the units of kW to find pumping power in kW. NOTE: The heat is removed from the system, so it should be negative in your equation! show all steps please

How can speed be attained from path function and time?