A stream of water flowing horizontally with the speed of 15m/s gushes out of a tube of cross-sectional area 10-2m2 and hits a vertical wall nerby. What is the force exerted on the wall by the impact of water assuming it does not rebound?
We know that speed of water is 15m/s so we can assume the tube height to be 15 m. Are of cross section is given... So volume of the cylinder(water flowing) can be calculated
Volume=0 .15 m^3
Density=mass/ volume.as density of water is 1000 kg/m^3..... Mass of water is 150 kg.
Force=mv-mu
=150(15) -150(0)
2250 N
Force = rate of change of momentum
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To find the force exerted on the wall by the impact of water, we can use the equation:
Force = Mass × Acceleration
First, let's find the mass of water hitting the wall per second. We can calculate the mass by multiplying the density of water (which is approximately 1000 kg/m³) by the volume of water passing through the cross-sectional area of the tube per second.
Volume = Cross-Sectional Area × Velocity
Substituting the given values into the equation, we get:
Volume = 10^(-2) m² × 15 m/s
Volume = 0.15 m³/s
Mass = Density × Volume
Mass = 1000 kg/m³ × 0.15 m³/s
Mass = 150 kg/s
Now, let's calculate the force exerted on the wall. The acceleration in this case is the change in velocity over time, which is equal to the velocity itself since the water does not bounce back. Thus, the acceleration is 15 m/s.
Force = Mass × Acceleration
Force = 150 kg/s × 15 m/s
Force = 2250 N
Therefore, the force exerted on the wall by the impact of water, assuming it does not rebound, is 2250 Newtons.