3.3.1. GATE 2005 Civil Engineering Problem

In the GATE 2005 civil engineering problem, there is a tank or deflector placed on a frictionless trolley. The water jet, which has a density of 1000 kg/m³, strikes the deflector and turns by 45 degrees. The velocity of the jet leaving the deflector is 4 m/s, and its discharge is 0.1 m³/s.

This section introduces the problem where a water jet emerges from a tank and hits a deflector on a trolley without friction. We note the important parameters: the density of the water (1000 kg/m³), the velocity at which it exits the deflector (4 m/s), the discharge rate (0.1 m³/s), and the angle (45 degrees). These values are crucial for applying momentum conservation principles in the later calculations.

Imagine a garden hose spraying water at an angle. The water flows out at a certain speed and hits a wooden fence, causing the fence to push away. This is similar to the problem where water flowing from a tank strikes a deflector and causes a reaction on the trolley.

Flow classification of the problem includes: one-dimensional, steady flow, and turbulent conditions. The flow is fixed control volume.

In this problem, the flow can be classified as one-dimensional because the water jet is primarily moving in one direction. It is also steady because the discharge rate and velocity do not change over time. The flow can be considered turbulent due to the high velocities involved. By identifying these factors, we can determine the appropriate equations to apply for conservation of momentum and mass.

Think of a straight river where water flows consistently in one direction. If you drop a rock in, the way the water disperses can show turbulence. In engineering, understanding whether the flow is steady or turbulent helps in predicting behavior when designing systems like bridges or pipes.

For momentum conservation, the sum of the forces equals the rate of change of momentum flux within the control volume, which corresponds to net outflux of momentum flux.

The key principle used here is the conservation of momentum, which states that the total momentum of a closed system remains constant unless acted upon by an external force. In this context, we analyze the forces acting on the control volume (the system we are examining). By identifying the water jet's momentum before and after hitting the deflector, we can calculate the force exerted on the trolley.

Imagine pushing a swing. If you give it a firm push (force), it swings back and forth (momentum). When the swing is at the highest point, it momentarily stops before reversing direction, similar to how momentum changes in the water jet's motion before and after striking the deflector.

Given values include velocity (V = 4 m/s), discharge (Q = 0.1 m³/s), and the angle (θ = 45°). Using these factors, we can compute the force recorded by the spring as follows: F = ρQV cos(θ).

We substitute the known values into the momentum equation calculated through the flow parameters: ρ is the density (1000 kg/m³), Q is the discharge, and V is the velocity. We apply the cosine of the angle (45 degrees) to find the effective force in the desired direction. Simplifying using these values yields the force on the spring, allowing us to analyze the effect of the water jet on the system.

Imagine using a slingshot. The more tension you build (like flow and pressure), the further the projectile goes. By knowing how much you pull back (velocity) and the angle you release, you can predict where it will land. This is similar to calculating the force in our problem through angles and velocity of the jet.

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