The fire tug discharges a stream of salt water (density 1030 kg / m^3 ) with a nozzle velocity o

step 1 So here on this problem we are given this diagram and we have to calculate the thrust T that mus

The fire tug discharges a stream of salt water (density 1030...

The fire tug discharges a stream of salt water (density $1030 \mathrm{kg} / \mathrm{m}^{3}$ ) with a nozzle velocity of $40 \mathrm{m} / \mathrm{s}$ at the rate of $0.080 \mathrm{m}^{3} / \mathrm{s}$. Calculate the propeller thrust $T$ which must be developed by the tug to maintain a fixed position while pumping.

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Key Concepts

Mass Flow Rate

Mass flow rate is the quantity of mass passing through a cross-sectional area per unit time. In fluid mechanics, it is calculated as the product of the fluid density and the volumetric flow rate. This concept is essential in determining how much mass is being accelerated or decelerated in flow systems.

Momentum Conservation

Momentum conservation, based on Newton's second law, states that the rate of change of momentum of a fluid is equal to the net applied force. In a fluid jet, the momentum carried by the moving fluid is used to calculate the force (or thrust) generated, which is crucial for understanding propulsion or reaction forces.

Thrust Calculation in Fluid Jets

Thrust in the context of fluid jets is determined by the product of the mass flow rate and the jet velocity. This relationship comes from the linear momentum flux of the fluid exiting the nozzle, indicating that a higher flow rate or velocity results in greater thrust. This concept is widely used in the design and analysis of engines and pumps, where maintaining force balance is critical.

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