Hydraulics - Engineering

Q1:

If jet of water coming out from a nozzle with a velocity 9.81 m/s, the angle of elevation being 30°, the time to reach the highest point is

A 0.25 s

B 0.50 s

C 1.0 s

D 1.5 s.

ANS:B - 0.50 s

To solve this problem, we can analyze the motion of the water jet using basic principles of physics. We'll consider the motion in the vertical direction. Given:

  • Initial velocity (u) = 9.81 m/s (upward)
  • Angle of elevation (θ) = 30°
We need to find the time taken (t) for the water jet to reach the highest point. The initial velocity can be split into horizontal and vertical components:
  • Ux=ucosθ
  • Uy=usinθ
Where:
  • ux​ is the horizontal component of velocity.
  • uy​ is the vertical component of velocity.
At the highest point, the vertical component of velocity becomes 0 because the water momentarily stops before falling back down due to gravity. We can use the equation of motion to find the time taken to reach the highest point: uy​=usinθ−gt Where:
  • g is the acceleration due to gravity (approximately 9.81 m/s^2).
At the highest point, uy​=0. So, we have: 0=usinθ−gt Solving for t: t=usinθ​/g Substituting the given values: t=9.81×sin⁡(30∘) / 9.81 =9.81×0.5 / 9.81 = 0.5  Therefore, the time taken to reach the highest point is 0.5s. Thus, the correct option is 0.50s.