Problem: The 3.0-cm-diameter water line in (Figure 1) splits into two 1.0-cm-diameter pipes. All pipes are circular and at the same elevation. At point A, the water speed is 2.0 m/s and the gauge pressure is 50 kPa .What is the gauge pressure at point B?

FREE Expert Solution

Bernoulli's equation:

$\overline{){{\mathbf{P}}}_{{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\rho }}{{{\mathbf{v}}}_{{\mathbf{1}}}}^{{\mathbf{2}}}{\mathbf{+}}{{\mathbf{h}}}_{{\mathbf{1}}}{\mathbf{\rho }}{\mathbf{g}}{\mathbf{=}}{{\mathbf{P}}}_{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\rho }}{{\mathbf{v}}_{\mathbf{2}}}^{{\mathbf{2}}}{\mathbf{+}}{{\mathbf{h}}}_{{\mathbf{2}}}{\mathbf{\rho }}{\mathbf{g}}}$

The volume of the cylindrical pipe, Vc = LA, where L is the length and A is the cross-sectional area.

The volume of water flowing through a cylindrical [ipe every second, Vw/s = LA/t

But we know that L/t = v, where v is velocity.

AvA = 2AvB

A = πr2

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Problem Details

The 3.0-cm-diameter water line in (Figure 1) splits into two 1.0-cm-diameter pipes. All pipes are circular and at the same elevation. At point A, the water speed is 2.0 m/s and the gauge pressure is 50 kPa .

What is the gauge pressure at point B?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Bernoulli's Equation concept. If you need more Bernoulli's Equation practice, you can also practice Bernoulli's Equation practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Pham's class at UCLA.