Propelling force due to an orifice

In summary, the problem involves a tank filled with water with an orifice at the bottom. The coefficient of discharge is given and the goal is to find the propelling force on the trolley when the orifice is opened. Using Newton's third law, the force on the trolley must equal the change in momentum of the liquid jet. However, there seems to be a calculation error with the velocity of the flow through the orifice. The correct velocity is 4.84 m/s, but it is unclear how this is relevant to the problem.
  • #1
Sia
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Homework Statement


A tank 1.5m high stands on a trolley and is full of water .it has an orifice of diameter 0.1m at 0.3m from the bottom of the tank.if the orifice is suddenly opened coefficient of discharge of the orifice is 0.60, then find propelling force on the trolley.
Ans: 67.39N

Homework Equations


F=c⋅ρ⋅A⋅v^2

The Attempt at a Solution


It looks like a simple problem based on Newton's third law of motion where the propelling force on the trolley must be equal to the change in momentum of the liquid jet coming out of the orfice.

thus F= 0.6X10^3X (Π/4)0.1^2X2X9.8X1.2
=110.35
which is not correct.

I am not getting what's wrong with my approach.
 
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  • #2
What is the velocity of the flow through the orifice ?
 
  • #3
Nidum said:
What is the velocity of the flow through the orifice ? Why is this relevant ?
velocity of the flow will be: √(2gh)=√(2X9.8X1.2) =4.84
didn't understand next part
 

1. What is a propelling force due to an orifice?

The propelling force due to an orifice is the force that is generated when a fluid, such as water or air, is forced through a small opening or orifice. This force is typically used to propel objects, such as rockets or water jets.

2. How does the size of the orifice affect the propelling force?

The size of the orifice directly affects the propelling force. A smaller orifice will result in a higher force due to the restriction of the fluid flow, while a larger orifice will result in a lower force due to the increased flow rate of the fluid.

3. What factors determine the magnitude of the propelling force?

The magnitude of the propelling force is determined by several factors, including the size and shape of the orifice, the density and velocity of the fluid, and the pressure difference across the orifice.

4. How is the propelling force calculated?

The propelling force can be calculated using the Bernoulli's equation, which takes into account the fluid's density, velocity, and pressure at different points along the orifice. Other equations, such as the Torricelli's theorem, can also be used to calculate the force depending on the specific scenario.

5. What are the practical applications of the propelling force due to an orifice?

The propelling force due to an orifice has various practical applications, including propulsion systems for rockets, water jets for marine vessels, and fuel injection systems for automobiles. It is also used in industries such as aerospace, automotive, and manufacturing for various purposes like cutting, drilling, and cleaning.

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