# Mechanical Engineering The sum of the static and dynamic pressures, homework help

1-The sum of the static and dynamic pressures is called the *stagnation pressure*. An airplane is flying at an altitude of 12,000 m where density of the atmospheric air is 0.312 kg/m^{3}. Determine the gage pressure in N/m^{2} at the stagnation point on the nose of the plane if the speed of the plane is 306.2 km/h.

2-A pump is used to lift the water from a large reservoir to 31.8 m above at a rate of 0.0332 m^{3}/s by a 15.3 kW pump. If the mechanical efficiency of the pump is 65.9 % determine the irreversible head loss (in meter) of the piping system. The density of water is 1000 kg/m^{3}. The flow is steady and incompressible.

3-The impeller of a centrifugal pump has inner and outer diameters of 13 and 30 cm, respectively, and a flow rate of 0.19 m^{3}/s at a rotational speed of 1200 rpm. The blade width of the impeller is 8 cm at the inlet and 3.5 cm at the outlet. If water enters the impeller in the radial direction and exits at an angle of 60° from the radial direction, determine the minimum powerrequirement in kW for the pump.

4-A helicopter of mass 12,000 kg hovers at sea level with a load of 11,952 kg. The horizontal blades above the helicopter cause a 18-m-diameter air mass to move downward at an average velocity proportional to the over-head blade rotational velocity (rpm). Determine the power input in kW required to hover with the load. Take the density of atmospheric air to be 1.18 kg/m^{3}. Assume air approaches the blades from the top through a large area with negligible velocity and air is forced by the blades to move down with a uniform velocity through an imaginary cylinder whose base is the blade span area. The elevation effects are negligible, and the frictional effects can be disregarded.

5-Determine the magnitude of acceleration at the location (4.7, 2.4) for the following steady, incompressible and two dimensional velocity field.

6-In a steady, incompressible and fully developed flow between two parallel plates where the top plate is moving and bottom plate is stationary, the velocity field can be represented as V= (Vy/d) i. V is the velocity of the top plate, d is the gap between two plates and y is the distance from the bottom plate toward the top plate. If the flow is rotational how much is the absolute (without ‘+’or ‘-’ sign) angular velocity in rad/s when the top plate is moving at a velocity 5.2 m/s and the gap between the plate is 0.85 m?

in this book chapter 4,5 and 6 you will find all needed materials to answer those questions.

Fluid Mechanics Fundamentals and Applications, 3rd Edition Cengel, Yunus; Cimbala, John, McGraw Hill

Please I need correct answer if you cant do this let others help me, Thank you.