## Garden Hose

Consider a typical garden hose produces a horizontal jet of water (density = 1,000 kg/m^3). Estimate the minimum force required to stop the water flow with your hand by pressing it perpendicularly against the nozzle's opening.

##
__
__**Hint**

**Hint**

$$$Q=vA$$$

where
$$Q$$
is the flow rate,
$$v$$
is the velocity, and
$$A$$
is the cross sectional area.

##
__
__**Hint 2**

**Hint 2**

Since the water jet is deflected perpendicularly, the required force must deflect the total horizontal momentum of the water.

$$$F=\rho Qv$$$

where
$$\rho$$
is the density,
$$Q$$
is the flow rate, and
$$v$$
is the fluid velocity.

Volumetric flow rate:

$$$Q=vA$$$

where
$$Q$$
is the flow rate,
$$v$$
is the velocity, and
$$A$$
is the cross sectional area.

$$$Q=vA=(0.1m^2)(20m/s)=2\:m^3/s$$$

Since the water jet is deflected perpendicularly, the required force must deflect the total horizontal momentum of the water.

$$$F=\rho Qv$$$

where
$$\rho$$
is the density,
$$Q$$
is the flow rate, and
$$v$$
is the fluid velocity. Thus,

$$$F=1,000\frac{kg}{m^3}\times 2\frac{m^3}{s} \times 20\frac{m}{s}=40,000\frac{kg\cdot m}{s^2}=40\:kN$$$

40 kN