Air flows steadily through a tee-piece of width w, as shown in Figure P4.49. Gravity is not important, and the air density ρ is constant. The flow exits to atmospheric pressure pa. If the resultant force acting on the tee-piece is zero: (a) Find the ratios V2/V1 and V3/V1 (these are numbers). (b) find the gauge pressure pig at the flange in terms of ρ, V1, h, and w.

Consider the steady flow of a fluid of constant density in a duct of constant width w. The fluid flows smoothly up a bump, as shown in Figure P4.41, and then separates such that the streamlines are initially straight and parallel. Determine the magnitude and the direction of the horizontal component of the force exerted by the fluid on the bump in terms of the density ρ, the inlet velocity V1, the inlet height H1 and the width w, given that the pressures and velocities at stations 1 and 2 are uniform across the heights H1 and H2, and that H1/H2 = 2.  

As shows a 100 g block of copper (ρ = 8900 kg/m3) and a 100 g block of aluminum (ρ = 2700 kg/m3) connected by a massless string that runs over two massless, frictionless pulleys. The two blocks exactly balance, since they have the same mass. Now suppose that the whole system is submerged in water. What will happen?A. The copper block will fall, the aluminum block will rise.B. The aluminum block will fall, the copper block will rise.C. Nothing will change.D. Both blocks will rise.

Using the data given in the schematic attached, find the difference of pressure PA and PB  h1= 0.65m     h2= 0.1m      h3= 0.75m      h4=  0.45m     Density of fluid A is  pA= 900kg/m3 Density of fluid B is  pB= 1034kg/m3 Mercury density is   pHg= 13600kg/m3 Oil density is  poil=  700kg/m3 (In the given figure, the pipelines are parallel to each other and not necessarily at the same height.)

In a closed subway car, a girl holds a helium-filled balloon by a string. While the car is traveling at constant velocity, the string of the balloon is exactly vertical. (Hint: For constant velocity, a buoyant force acts upward, but for constant deceleration, the buoyant force becomes tilted, but remains antiparallel to the tension.)a) While the subway car is braking, will the string be inclined forward or backward relative to the car? b) Suppose that the string is inclined at an angle of 20° with the vertical and remains there. What is the acceleration of the car?

A one-dimensional air flow of constant density ρ exits steadily into the ambient atmosphere from the contraction shown in Figure P4.19. The contraction is bolted onto a constant area duct at station 1, and the area ratio A1/A2 = 4. If the total force in the bolts is Fx, find . Show all your work, and state your assumptions clearly. Would your analysis hold if the flow direction was reversed?  

Consider a cylindrical tank of height h and base radius r filled with a liquid of density ρ. Find the hydrostatic Force exerted by the liquid on one side of the base of the tank when the tank is completely filled. Given: h = 5 meters r = 2 meters ρ = 1000 kg/m^3 (density of water, for example)

How do you find the external forces' resultant?

A hydraulic press is composed of two cylindrical reservoirs of R1 and R2 rays.The plungers in this press are extremely light and can move virtually frictionless and perfectly adjusted to their respective cylinders. The fluid that fills the press reservoirs is low density and can be considered incompressible. When in balance, the F2 force supported by the larger plunger is 100 times higher than the F1 force supported by the smaller one. Thus, the R2 / R1 ratio between the rays of the emboli, is worth approximately:a) 100b) 50c) 10d) 1000e) 200

In the hydroelectric power plant whose cross-section is given, the flow rate of Q=33.045 m^3/sec is transmitted to the power plant through a D=1.6 meter diameter penstock. Ignoring friction losses; a) Find the internal pipe pressure at point 2 ( at the below ). b) Find the resultant force (F) and its direction (O) that the water exerts on the fixation mass. c) Calculate the electrical power generated in the plant. (Pwater= 1 ton/m^3, Ywater= 9.81 kN/m^3, g=9.81m/s^2, Beta= 45 degree