Answer to Question #264981 in Mechanical Engineering for LEE

Question

1, In a hydroelectric power plant, water enters the turbine nozzles at 800 kPa absolute with a low velocity. If the nozzle outlets are exposed to atmospheric pressure of 100 kPa, determine the maximum velocity to which water can be accelerated by the nozzles before striking the turbine blades.

2, An airplane is flying at an altitude of 12,000 m. Determine the gage pressure at the stagnation point on the nose of the plane if the speed of the plane is 300 km/h.

Answer 1

Pressure (atmospheric) = 100 kPa

So. we solve for the maximum velocity (m/s) to which water can be accelerated by the nozzles

Now,

$Pabs =Patm + Pgauge = 800 KN/m²$

Thus

$\frac{PT}{9.81} + \frac{ VT²}{2g} =\frac{PN}{9.81} + \frac{VN²}{2g}$

Here

Acceleration due to gravity = 9.81 m/s

$\frac{800}{9.81} + 0= \frac{100}{9.81} + \frac{VN²}{19.62}$

Here,

$9.81 * 2= 19.62$

Thus,

$\frac{VN²}{19.62} = \frac{700}{9.81}$

So,

$VN² =1400$

$VN =37.416 m/s$