The fire boat discharges two streams of seawater, each at a...

The fire boat discharges two streams of seawater, each at a flow of $0.25 \mathrm{m}^{3} / \mathrm{s}$ and with a nozzle velocity of $50 \mathrm{m} / \mathrm{s}$ Determine the tension developed in the anchor chain, needed to secure the boat. The density of seawater is $\rho_{\mathrm{se}}=1020 \mathrm{kg} / \mathrm{m}^{3}$.

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Key Concepts

Conservation of Momentum

This principle states that the total momentum in a closed system remains constant if no external forces act on it. In problems involving fluid jets, conservation of momentum is used to relate the momentum of the discharged fluid to the reaction force exerted on the system, such as the boat anchoring mechanism.

Mass Flow Rate

Mass flow rate is the product of the fluid's density and its volumetric flow rate. It quantifies the mass of fluid passing a given point per unit time, which is essential in calculating the momentum change of the fluid and thereby the reaction force since the force is directly proportional to the mass flow rate times the fluid velocity.

Newton's Third Law

Newton's Third Law asserts that for every action, there is an equal and opposite reaction. In the context of the fire boat discharging water, the force exerted by the outgoing water jet (action) results in an equal and opposite force (reaction) on the boat, which needs to be countered by the tension in the anchor chain.

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