Evaluation

Input	Output
A pipe of radius R has a fully developed laminarflow of air at P0, T0 with a velocity profile of V = Vc[1 - (r/R)2], where Vc is the velocity on the center-line and r is the radius, as shown in <image 1>. Find the total mass flow rate and the average velocity, both as functions of Vc and R. (A) $\begin{aligned}V&=\frac{V_c}{3}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^2\\\\\end{aligned}$ (B) $\begin{aligned}V&=\frac{V_c}{2}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^2\\\\\end{aligned}$ (C) $\begin{aligned}V&=\frac{V_c}{2}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^3\\\\\end{aligned}$ Answer with the option's letter from the given choices directly. No punctuation.	Google: Gemini Pro Vision 1.0 mmmu / Energy_and_PowerPublic (A) Expected Answer: B Difficulty: Hard Subfield: Thermodynamics

Input

Output

A pipe of radius R has a fully developed laminarflow of air at P0, T0 with a velocity profile of V = Vc[1 - (r/R)2], where Vc is the velocity on the center-line and r is the radius, as shown in <image 1>. Find the total mass flow rate and the average velocity, both as functions of Vc and R.

(A) $\begin{aligned}V&=\frac{V_c}{3}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^2\\\\\end{aligned}$

(B) $\begin{aligned}V&=\frac{V_c}{2}\\\dot{m}&=\frac{\pi}{2\cdot\nu}\cdot V_c\cdot R^2\\\\\end{aligned}$

Answer with the option's letter from the given choices directly. No punctuation.

Google: Gemini Pro Vision 1.0

mmmu / Energy_and_PowerPublic

(A)

Expected Answer: B

Difficulty: Hard

Subfield: Thermodynamics

Evaluation ID: 3a59c213-8e4d-40c6-ad2a-d7709c675546
Created: February 21, 2024

Raw Output

{
  "id": "gen-KciqeOpNb4j8DJuADhDjynornzrV",
  "model": "google/gemini-pro-vision",
  "choices": [
    {
      "message": {
        "role": "assistant",
        "content": " (A)"
      },
      "finish_reason": "STOP"
    }
  ],
  "object": "chat.completion",
  "created": 1708556815,
  "usage": {
    "prompt_tokens": 2024,
    "completion_tokens": 12,
    "total_tokens": 2036
  }
}